It’s official: The building that has housed the Princeton post office on Palmer Square since 1934 is for sale. A sign advertising the availability of the 11,500-square-foot building on the green was scheduled to be posted on Tuesday.

Numerous entities have shown interest in the prized piece of real estate since the financially strapped United States Postal Service (USPS) announced last year that it was going to sell the building as part of its streamlining efforts. The facility would be relocated to another downtown site as part of the plan. One scenario would have the post office remaining in a small section of the building, but only if a buyer were to divide it up for multiple uses. And that possibility seems remote.

“We’ve seen a lot of interest in the site,” said Alec Monaghan, the broker with CBRE, the global real estate firm marketing the building. “We still don’t know where the post office is going. We have a few potential good alternatives in town that are more modern and would serve the public better. One consideration could have them remaining in the building if it was a mixed use kind of thing. A gallery has been mentioned. But I think it’s better for the office to come out of there, so it probably won’t be staying in the building.”

Among the bidders for the property is Palmer Square Management, which oversees the tenants of the square. “Hopefully, we’ll be able to buy it and diversify the tenant mix of Palmer Square,” said David Newton, vice president of the company. “Whether in terms of retail or dining or some other use, we see the building very much as a central part of the asset. Hopefully, it would be used to enhance both the square and The Nassau Inn.”

Mr. Newton said he would like to see a new look for Palmer Square East, which the rear of the building faces. “What is now the loading dock would be totally cleaned up so you present some form of retail facade,” he said. “ The front of the building, which faces the green, “is more problematic for us,” Mr. Newton added. “We don’t want to share the green, other than with shoppers and the public. We’ve put a lot of effort into maintaining it. The post office has been a very good neighbor and very low impact. We’re sad to lose them.”

The post office was the first building to open on Palmer Square, which was originally designed to include municipal buildings as well as retail establishments. “It was contemplated whether they should put Borough Hall on the green,” Mr. Newton said. “So it was always meant to be a place where central services meet with other, more mundane uses. That all of a sudden disappears, and now it goes to the highest bidder. So it’s not a particularly happy circumstance for us.”

Mr. Monaghan declined to reveal the names of any other bidders for the property, but said he imagined the buyer would be “a combination of a restaurant and retail, all retail, or gallery space. It’s really up to the purchaser,” he said. “I think a restaurant would be one of the highest and best uses. It could also be used for a company that wants to have a presence in Princeton, like a hedge fund.”

The offering of the post office building was originally supposed to be announced last month, but was postponed to allow the municipality to make sure its historical features were being properly considered. A 1939 mural depicting Native Americans reacting to the arrival of European colonists, a scene that has caused controversy in recent years because some consider it to be racist, is among the building’s historical points of interest.

The post office is listed on the state and national registers of historic places as contributing to the Princeton historic district. The postal service has agreed to put an easement on the building, and is working with the New Jersey Historic Trust. But according to a spokesperson for the Trust, the easement cannot be recorded until the building is sold.

“The building is a beautiful asset that needs to be respected, and it needs to end up with the right purchaser,” said Mr. Monaghan, who lives in Princeton. “So it’s not just the highest price. That’s our charge with the post office, but clearly it will be respectful of the town.”