The Mexico international enjoys great popularity in the US and is wanted in Texas.
Austin will have an MLS franchise in 2021, and the Texas-based club's owner, Anthony Precourt, admits an interest.
He said, “Chicharito would be pretty special; I'd be as excited as anyone.That's the type of player we'll target, and we'll give our best pitch.
“I think he's got a year left on his contract at West Ham and I think other clubs are rumoured to be looking at him in MLS.
“We'll certainly be active in trying to recruit him in the years to come."