Los Angeles has thrown its hat into the ring to host the prospective George Lucas Museum, with opposing bids coming from both Chicago and San Francisco.

Mayor Eric Garcetti has launched a campaign to bring the Lucas Museum of Cultural Arts – a legacy project of Star Wars and Indiana Jones creator George Lucas – to Los Angeles, which will cost around US$300m (€220m, £179m) to build.

The mayor is offering a site in Exposition Park, the equivalent to Chicago’s Museum Campus and home to the Los Angeles Memorial Coliseum.

Garcetti asked Lucas to consider Los Angeles because it is “a place where its impact can be amplified like no other,” with the mayor also using the hashtag #WhyLucasInLA to promote the cause.

Lucas looked to be initially veering towards a bid from San Francisco, but Chicago and Los Angeles are now providing fierce competition to the bid.

San Francisco has responded to the Los Angeles bid by rolling out the welcome mat for Lucas, hanging banners reading “George Lucas, please build your museum in San Francisco for the world to enjoy” at both San Francisco City Hall and in the area of the proposed site for the museum.

Lucas has said he plans to invest up to US$300m (€220m, £179m) in the project, with another US$400m (€294m, £238m) endowment coming when he dies.