The deadline for offers to purchase the Palmer Square post office came and went last Friday, and “a number of interested parties” are being considered, according to a spokesman for the real estate firm handling the sale of the office and several such locations across the country.

While he declined to disclose just who is in the running, Alec Monaghan, first vice president of the global firm CBRE Inc., said, “These are broadly retail uses, compatible with the rest of Palmer Square.” Interest has come from both within and outside of New Jersey, he added, confirming that Palmer Square Management, which oversees the tenants of the Square, is among the bidders.

The building that has housed the Princeton Post office since 1934 was officially placed on the market this past September. The prime piece of real estate is being sold by the United States Postal Service as part of its nationwide streamlining efforts. A restaurant, retail, and gallery space have all been mentioned as possible uses for the space, which includes a historic mural painted in 1939, depicting Native Americans reacting to the arrival of European colonists.

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

A second round of offers will be conducted for the interested buyers this week. “The idea is to tighten everything up in terms of their purchase price, due diligence, and that kind of thing,” Mr. Monaghan said. “Within the next several weeks, we’ll look to be getting a lead bidder.”

In the meantime, the real estate firm has identified a few downtown locations as possible sites for the local post office once the Palmer Square building is sold. “We believe we have three or four good possible locations,” Mr. Monaghan said. “But if there is anyone out there with a 2,000-square-foot, ground floor retail space that we’ve missed, we’re certainly open to considering it.”

Asked whether a relocation to Princeton Shopping Center or another location with ample parking was also being considered, Mr. Monaghan said it was not. “I think a place like that is dislocated from town,” he said. “While the parking is one thing that would work, it misses on a lot of other fronts. Princeton University students and a number of commercial accounts are among the walk-in traffic. I think the parking can be figured out and satisfied in a downtown location. Princeton deserves a post office downtown.”

Mr. Monaghan said one of the locations under consideration is on Nassau Street, but declined to identify the other sites. “We’re using Palmer Square as a center point, and going from there,” he said.