The 19-year-old midfielder has been outstanding for the Bairns since breaking into the first team in 2007, and has been called into the Scotland Under 21 set-up.
Skysports.com understands up to 12 clubs from the Premier League and Championship are regularly checking on him and Falkirk could face a battle to keep him at the club.
Arfield is, though, on a long-term contract after penning a five-year deal earlier this year, but with United and Chelsea leading the chase, the Bairns could easily cash in on their prized asset.