The 21-year-old, who was born in Utah, joined Bayern Munich in 2019, representing their second team on 27 occasions in all competitions, but he failed to make the breakthrough into the senior side, only featuring once for the first team in the DFB-Pokal in August 2021.
Booth moved to Dutch outfit Utrecht last summer, and he has impressed during the 2022-23 campaign, scoring twice and registering three assists in 16 appearances for the club.
The former United States Under-19s international has made 14 appearances in the Eredivisie this season, scoring twice and contributing three assists.
According to the Daily Mail, Man United boss Ten Hag is an admirer of the midfielder, who is now being tracked by the 20-time English champions.
The report claims that a number of other English teams, in addition to sides from Spain and Italy, are keeping a close eye on his performances in the Netherlands this season.
"I'm just enjoying it. I'm playing every week at a good level and I want to make the most of every moment," the newspaper quotes Booth as saying.
"I'm flattered if the national teams of USA or Italy think about me or clubs in the Premier League, La Liga or Serie A. Since I was a little boy playing soccer in the basement of our home in Eden, I've always said you can't dream big enough."
Utrecht agreed a pre-contract with Booth last January, and they have the central midfielder on a deal until June 2025, putting them in a strong position when it comes to his future.
Man United boosted their midfield last summer with the arrivals of Casemiro and Christin Eriksen, but there could be departures in that area of the field at the end of the season.
Scott McTominay was heavily linked with a January exit, and the Scotland international could decide to leave Old Trafford in the upcoming market in search of regular starts.
An exit for McTominay could open the door for Man United to move for Taylor, with the American potentially viewed as a low-cost option in the middle of the park.
The 20-time English champions are planning to be active this summer, although there will have to be some first-team departures, with Harry Maguire also among those thought to be heading for the exit door.
Man United will be bidding to return to winning ways in the Premier League when they welcome Crystal Palace to Old Trafford on Saturday afternoon.