The long-time United employee is close to agreeing a deal with Minnesota United, as per The Athletic.
The deal would see the 32-year-old become Major League Soccer's youngest-ever head coach, overtaking Roy Wegerle, also 32 when he took over the Colorado Rapids in 1996, by a matter of months.
Welshman Ramsay has long been rated as an up-and-coming talent in British coaching, with Wales manager Rob Page singing his praises.
Ramsay worked as an assistant with the national side in 2023, and Page commented, "He's arguably one of the best young coaches in football at this moment in time."
The Shrewsbury-born coach previously led Chelsea's Under-23s before joining United under Ole Gunnar Solskjaer's tenure.
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Initially arriving as set-piece coach, he rose in importance and is now listed by the club as an 'Individual Coach'.
Erik ten Hag restructured his coaching staff after arriving at United in 2022, bringing in former England manager Steve McLaren as an assistant.
Ramsay remained among the changes, but now looks set to head stateside.
The MLS is currently in its winter break, with the 2024 season to kick off on February 22nd as Lionel Messi's Inter Miami take on Real Salt Lake.
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Last season Minnesota finished 11th in the Western Conference and missed out on the play-offs.