BankBoston Corp. is hoping to provide funding for a convention center in downtown Boston and, in exchange, could get naming rights.

The $62 billion-asset banking company said it would be willing to give a last-minute gift of less than $20 million to help close the gap between what the city and the state are willing to pay for the $700 million construction project.

A bank spokeswoman said the funding proposal was made to insure that the project would go through.

Last week, the state House of Representatives approved a bill to fund the state's share.

Boston Mayor Thomas M. Menino struck a compromise with House Speaker Thomas Finneran on legislation that would have the city put up $157.8 million to buy the site for the project. Under the agreement, the state would put up $500 million. If construction costs exceed $205 million, the city and state agreed to split additional expenses.

But BankBoston's ultimate role has yet to be determined, said the bank's spokeswoman. The outcome probably won't be decided until the state Senate takes up its own version of the bill this month.

If accepted, BankBoston's proposal could lead to its getting naming rights for the new facility, The bank would follow in the footsteps of many institutions that have attached their names to sports arenas and civic centers in exchange for financing.

Fleet Financial Group beat out BankBoston in the bidding two years ago for the right to put its name on the new Boston Garden. The building is now known as the Fleet Arena.

Other banking companies have put their names on civic centers, for example, PNC Bank Corp., which has its name on the former Garden State Arts Center in New Jersey.

Consultants said such arrangements translate into highly valuable brand- name positioning for banks.

"It's a marketer's dream," said Gary Stibel, principal and founder of New England Consulting Group in Westport, Conn. "Every time the people who live in the area walk by there, they will be reminded of how BankBoston helped their community."

The convention center is to be built in South Boston, near the financial district where BankBoston has its headquarters.

Civic leaders said the convention center would create many jobs and boost local businesses that rely on tourism. "It's been our No. 1 priority," said a spokesman for the Greater Boston Chamber of Commerce.

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