When Lawrence I. Linksman assembled a small group of investors last July to buy the former Times Tower, known as One Times Square, he did not anticipate the avalanche of publicity that seems to come with the building. He says that if he had known, ''I would have hired an agent instead of an architect.''

Mr. Linksman, the director of TSNY Realty Corporation, has been asked to appear on television and radio news programs, has agreed to let filmmakers shoot scenes for a movie starring Roger Moore in which a character plunges from the building into the New Years Eve crowd below, and conceived the idea of redesigning the Great Ball as a Big Apple.

But he bought the building from Kemekod, a Swiss company, ''strictly as an investment property, based on what profit I thought I could make,'' he said. He brought together several investors who put up $2 million in cash to buy the building for a total price of $12 million, he said. He also manages the building.

At the age of 27 Mr. Linksman has already acquired an ownership interest in several buildings. He grew up in Brooklyn and graduated from the State University of New York at Binghamton with a degree in accounting in 1976. H e joined the mortgage brokerage company owned by the M.A.C. Organization, in New York, where he says he learned ''what makes a building profitable.'' With associates from the firm he formed a m anagement company and eventually began to buy properties.

When Mr. Linksman bought One Times Square, it was about 70 percent occupied, he said. Almost all the tenants were on month-to-month leases, mostly at rents of $8 to $10 a square foot per year.

''I went in there and explained that because of the cost of the building, $25 a square foot was the lowest rent I could accept,'' he said, and that he has converted 30 percent of his tenants to threeyear leases at about $25 a square foot.

For the most desirable space, the 5,000-square foot floors in the ''tower'' section, he is asking about $40 a square foot. The 22d floor is already rented to Krypton Films at that rent, he said.

Real estate professionals familiar with the office market in the Times Square area expressed surprise that so high a rent was achievable, although they said rents have been gradually rising. In the former Knickerbocker Hotel at 1461 Broadway, a building on the southeast corner of Broadway and 42d Street that was recently converted to office space, units began renting at about $15 a square foot last year, a spokesman for the manangement said, but recent leases have been signed at about $20 a square foot.

Other brokers said that asking rents for space in better buildings near Times Square ranged between $25 and $35 a square foot. At One Times Square, the top two floors of the lower tower, formerly occupied by the Act One restaurant, are also available for rent. But Mr. Linksman said he doubted that another restaurant would move in to the 17,000 square feet of space, mainly because of the cost of providing 24-hour security and heat for just one tenant.

When the Times building went up at the Crossroads of the World in 1905, it was the city's second tallest skyscraper. It had an elaborate terra-cotta facade designed by C.L.W. Eidlitz and Andrew C. McKenzie, and it soon acquired its own traditions, such as the wraparound news sign and the dropping of the Great Ball, begun in 1908.

The Times sold the property in 1961 to Douglas Leigh, designer of many of the area's spectacular neon signs, who in turn sold it to the Allied Chemical Corporation. Allied stripped the building down to its steel frame a nd clad it in white marble in a $10 million renovation. Then in 1974 Allied sold the building to Alex Parker, a real-estate developer, for $6.25 million.

Leon Charney, a lawyer who represented the Kenekod group, said that he signed a contract to buy One Times Square from Mr. Parker for $8.2 million, but immediately resold the contract to the Swiss company for the same price, becoming a trustee-owner. He and the foreign investors sold it five months later to Mr. Linksman.

The Swiss company holds a $3.2 million second mortgage on the building. Mr. Charney holds a mortgage of $500,000. Mr. Parker holds a $6.1 million first mortgage.

Mr. Linksman's plans for the 22-story tower include a wraparound glass arcade for retail shops on the ground floor, costing a million dollars, and a new entrance on 42nd Street, which, along with the cleaning of the facade, will cost another million dollars.

The proposed glass-enclosed arcade was designed by Michael Lynn & Associates. It would encircle the building, including the small island and kiosk owned by the city just north of 43d street, which he hopes to lease from the city by offering comparable space inside the building. Mr. Linksman said bright interior lighting would illuminate the entire area. He said he was working with the Urban Development Corporation on the plans, which could include a north-south walkway running through the building to provide access to shops.

Another change likely to occur in the appearance of the building under its new owner is the addition of a series of electronic computerized signs above the one already in place on the north side of the building. Mr. Linksman said that when he bought the building he was unaware that its north face is considered ''the most desirable sign location in the world,'' and it had never occurred to him to rent out the side of a building before. He said the revolving news or ''zipper'' sign will be reinstated, and that its annual operating cost of over $300,00 will be shared by several companies.

Mr. Linksman is among those investors who is looking forward to the redevelopment of Times Square, and feels that One Times Square will benefit from its position at the center of it. The Urban Development Corporation is planning to take bids from developers for the construction of four office towers and the renovation of several theaters and the Times Square subway station. The estimated completion date for these projects is 1988, but Mr. Linksman thinks it can happen before that.

''The change in this area will take place soon,'' he said. ''I notice the di fference now - I work here until eight or nine every night, and it 's much safer, there are a lot more policemen.''

Mr. Linksman says that his adjustment to the attention of the news media has been difficult. But he is learning. His much publicized threat to darken the Great Ball if no company would underwrite the cost was an empty one, he admits. The ploy worked: WMCA radio station agreed to put up over $90,000 to cover the redesign of the ball and the cost of dropping it.

''It is hard to imagine a million people out there,'' he said, smiling, ''and no ball dropping.''

Illustrations: photo of Lawrence Linksman at Times Square