The friendship between Kelly and Belichick is well known, ever since Kelly's days when he established a fast-tempo offense as head coach at Oregon.
Kelly's trip to New England came after the Jacksonville Jaguars decided this week to stay with Nathaniel Hackett as offensive coordinator, a league source told ESPN's Chris Mortensen.
Patriots offensive coordinator Josh McDaniels took his name out of the running for the 49ers' head-coaching job on Monday, deciding to stay with the Patriots for the 2017 season.
The speculation is that Kelly could be an offensive assistant with the Patriots, or he's making a trip just to get some advice from his friend.
Kelly guided Oregon to the national championship game before leaving the Ducks for the NFL.
Kelly was fired by the Eagles less than three seasons into his tenure as head coach in December 2015, but remained out of work only one month before the 49ers hired him last January.
Kelly was fired at the end of the 2016 season after the 49ers finished 2-14 in his lone year in San Francisco.
Kelly, 53, owns a 28-35 record in four seasons as an NFL coach.