Hannibal is with the Man United squad in the United States preparing for their upcoming friendly fixtures with Arsenal, Real Betis and Liverpool.
The 21-year-old has featured in both of the team's pre-season games this summer, including the second half of their 2-0 victory over Rangers on Saturday afternoon.
However, Hannibal is not believed to be in the plans of Red Devils head coach Erik ten Hag for the 2024-25 campaign, with the club said to be prepared to let him leave.
According to Africafoot, Rangers have 'requested the loan' of Hannibal, with the club impressed by his performance against them in last weekend's friendly fixture.
Rangers 'battling' for Hannibal signature
The report claims that Copenhagen had been more advanced on a deal, but the Tunisia international is not interested in making the move to the Danish club.
Rangers, though, are thought to appeal to the midfielder, with the Scottish team's head coach Philippe Clement making him a priority target this summer.
Hannibal arrived at Old Trafford from Monaco in 2019, and he made his senior debut for the 20-time English champions at the end of the 2020-21 campaign.
The midfielder played 10 times for Ten Hag's side in the first half of the 2023-24 season, but he was allowed to join Sevilla on loan in January with an option to buy.
Hannibal struggled to make his mark at Sevilla
Sevilla could have made the switch permanent for around €20m (£16.9m) this summer, but the Spanish outfit decided against a move due to Hannibal's struggles at Estadio Ramon.
The midfielder was restricted to just six appearances for the Spanish club, and he headed back to Old Trafford once the loan deal had expired.
Hannibal is currently with the Man United first team, but the likes of Casemiro, Bruno Fernandes, Kobbie Mainoo, Christian Eriksen and Scott McTominay are all ahead of him in the pecking order.
Toby Collyer, 20, could be promoted to the senior group next season to boost the midfield competition, while the club are bidding to add a player in that area of the field before the transfer window closes.
As a result, it appears likely that Hannibal will be on the move, and a switch to Rangers could be the perfect fit for a player who desperately needs a consistent run of matches at this stage of his career.