The 17-year-old, who came through the youth system at Peterborough, has made 13 first-team appearances during the 2019-20 campaign, scoring twice.
The League One side's director of football Barry Fry confirmed that United, Arsenal and Liverpool were monitoring the teenager's progress in January, but Jones has vowed to remain focused on his development.
"As a 17-year old hearing that is really nice. I'm in a good position right now and I'm enjoying football so it doesn't distract me. It just gives me more motivation to show everyone what I can do," the attacker told Sky Sports News.
Jones made his League One debut against Burton Albion in November, while he has scored against Stevenage and Burnley in the FA Cup during the 2019-20 campaign.
Leeds United are also believed to be keeping a close eye on his development.