SAN FRANCISCO -- San Francisco Mayor Edwin Lee isn't about to lose a museum to be filled with George Lucas' lifetime art collection and movie memorabilia to another city.

The San Francisco mayor has given his staff until the end of May to come up with a list of places -- both private and public -- to present the "Star Wars" creator as possible locations in the city for the museum.

Lee said in a statement that he is well aware that San Francisco is in competition with another city. Chicago Mayor Rahm Emanuel in April gave orders to a dozen civic leaders, telling them to find a place in that city for Lucas' interactive museum and collection. This is a one-time opportunity for San Francisco, Lee said.

"I will not let go easily of such a significant private investment by one of the world's most prominent filmmakers," Lee said.

Raised in Modesto, California, Lucas has said he doesn't have enough wall space at his 6,000-acre (2,428-hectare) Skywalker Ranch in Marin County, California, and he intends to invest up to $300 million of his money for the Lucas Cultural Arts Museum with another $400 million endowment upon his death.

Earlier this year, the Presidio Trust rejected Lucas' proposal to open the museum on park land at the base of San Francisco's Golden Gate Bridge, which then offered him another location near the home of Lucasfilm's special-effects, game unit and corporate offices. Lucas is considering that offer.

Yet Chicago is considered a front runner for the display of Lucas' collection in part because he is married to Chicago businesswoman Mellody Hobson.