Booth, 20, recently made his first team debut for Bayern in a 12-0 win over Bremer SV in the DFB Pokal, and Bayern have been impressed with Booth's play in preseason.
However, with Booth's contract expiring in 10 months, he could sign a pre-contract with another club in four months.
Sources told ESPN in July that Bayern was interested in extending his contract, but a deal hasn't yet been completed.
The Eden, Utah native joined Bayern's youth setup from Real Salt Lake's academy in 2019. Burnley chairman Alan Pace served as interim Real Salt Lake president from 2006-08.
Booth then appeared for the club's Under-19 team as well as Bayern Munich II, which competes in the 3. Liga. Booth made two league appearances with Bayern Munich II last season, with an additional three appearances during the 2021-22 campaign.
Booth spent the latter half of the 2020-21 season on loan in the Austrian Bundesliga with St. Polten. He scored three goals in 17 league and playoff appearances, but it wasn't enough to prevent the club's relegation to the Austrian second tier.
Booth was in contention to take part in the U.S. men's national team's camp in Switzerland back in May. But club commitments in the form of a relegation playoff with St. Polten meant he was unable to participate.