The 21-year old Tunisia international has one year left on contract but Burnley have been pushing to sign him on loan with an obligation to buy next summer.
Mejbri impressed in United's older academy teams following his 2019 move from Monaco and was largely well-liked by club supporters who were excited to see him move into the first-team.
He later made his debut under Ole Gunnar Solskjaer in a 2-1 win over Wolves three-years ago before being eventually being loaned out to a variety of clubs.
Leeds United had also asked about Mejbri but are working on another midfield target with Cologne's Dean Lubijic the subject of offers from the Elland Road side.
Manchester United and Burnley are close to agreement on a deal for midfielder Hannibal Mejbri
Mejbri had a difficult loan with Sevilla earlier this year, where he endured a tense period at the LaLiga side before returning to Erik ten Hag's squad for pre-season training.
The youngster is now intent on leaving United to kickstart his career and plans to do so under Scott Parker at Burnley in England's second-division.
The deal will also include a sell-on clause as United continue their summer clear-out of fringe players at United.
Meanwhile, Old Trafford chiefs remain intent on boosting the team's midfield with their pursuit for PSG's Manuel Ugarte ongoing.