Oxford Development Co. has approached four to five companies about anchoring a proposed $238 million, 33-story skyscraper Downtown and is confident that it can get one to sign on.

“Our project, we feel, is definitely still in play,” said Shawn Fox, director of business development for Oxford.

The developer has either talked to or sent information about the proposed high-rise to four to five potential tenants looking for at least 250,000 square feet of space Downtown or in some other part of the region.

Mr. Fox would not say Wednesday which companies Oxford is trying to woo. But in announcing the project in May, Steve Guy, Oxford’s president and CEO, said the developer was talking to both national and local companies about becoming the anchor.

One potential tenant could be U.S. Steel Corp., which is considering a move out of U.S. Steel Tower when its lease expires in 2017.

Mr. Guy said in May that Oxford had discussed the project with U.S. Steel but that the steel maker had not indicated whether it was interested. U.S. Steel officials could not be reached for comment Wednesday.

Two energy companies, Chevron and Shell Oil Co., also could be interested in Downtown as they scout for more space in the region. Oxford has been trying to court one of those firms or another energy company to anchor the high-rise.

Mr. Guy said in May that one hindrance with the energy companies is the city’s ban on natural gas drilling, enacted by city council in 2010. He said at the time that the ban comes up in every conversation and that “the energy companies have just simply said, ‘We’re not doing business in the city.’ ”

The skyscraper would be built at the site of 441 Smithfield St., a seven-story Oxford-owned office building that is about three quarters empty. The building would be demolished to make way for the high-rise.

If Oxford can’t find an anchor tenant, it will scrap the high-rise in favor of a $40 million renovation of 441 Smithfield that would include 180,000 square feet of top-tier class A office space and 20,000 square feet of retail space.

Mr. Fox said the firm likely will decide on a course within the next couple of months. He said the decision will ride on whether Oxford can land a deal with an anchor and whether it can secure a $15 million state redevelopment assistance capital grant to help finance the project.

“We’re optimistic that we can do [the high-rise] if those things can come together,” he said.

Receiving the state capital assistance, he added, is “crucial” to the high-rise and the retrofit. “Projects of that size require public help with the infrastructure,” he said.