Filner, a Democrat, said that he plans to ask the former Republican presidential nominee to be honorary chairman of the bid for the 2024 Summer Games.
"Wouldn't he give instant credibility to it? He has some experience with Olympics," Filner said.
Romney oversaw the 2002 Winter Olympics in Salt Lake City, Utah. He also owns a house in San Diego's wealthy La Jolla coastal area.
A message to Marriott International Inc., where Romney is a board member, and an email to a Romney aide werent' immediately returned Saturday.
Filner said that he and Tijuana Mayor Carlos Bustamante hope to name a binational committee next week to lead the effort.
The U.S. Olympic Committee is talking to 10 cities about a possible bid for the games. Following failed U.S. bids for the 2012 and 2016 Olympics, the USOC sent out letters to 35 American cities in February to gauge interest in a potential run for 2024.
Los Angeles, which hosted the 1932 and 1984 Olympics, and Philadelphia have announced their interest.
The mayor of Tulsa, Okla., Dewey Bartlett, told the USOC in a letter last month the city would be interested in submitting a bid with a "Native America theme."
The United States hasn't hosted a Summer Olympics since the 1996 Atlanta Games.