Plans to sell the naming rights to the 170m (560ft) tower are set to be approved by the city council.
An un-named "premium brand" has expressed a desire to acquire the rights in time for the America's Cup World Series sailing event in July.
The local authority said it was maximising the "advertising potential" of its assets.
Portsmouth City Council's proposals are to agree the naming rights for five years, with the first changes to branding and signage in place by 17 July.
They are set to be approved as a key decision by the cabinet member for economic development on Friday.
The tower, which opened in 2005, is owned by the council and run by a private attractions management company.
A council report said the authority had been looking for ideas to "generate additional revenue by using the advertising potential of council-owned land and other assets" since 2009.
The display of the company's name on the exterior of the tower would constitute an advertisement and would have to go through the planning process.
Portsmouth's Spinnaker Tower could be rebranded with the name of a commercial sponsor within weeks.