The 20-year-old's contract at Old Trafford has been extended until June 2025, and he been regularly involved with the first team this season, featuring on 11 occasions in all competitions.
Man United head coach Erik ten Hag is said to be a huge admirer of Hannibal, but it has been decided that he needs regular football in the second half of the season to continue his development.
Sevilla continue to be heavily linked with the midfielder, but it is understood that Everton are attempting to hijack the move, with Toffees head coach Sean Dyche keen on him.
Earlier this week, The Sun reported that Everton were at the head of the queue for Hannibal, with Dyche determined to bring him to Goodison Park for the second half of the campaign.
Man United are said to be keen for Hannibal to remain in the Premier League, and a successful loan spell at Everton could see him become a regular for the Red Devils next season.
Hannibal is not representing Tunisia at the Africa Cup of Nations, with the midfielder allegedly deciding that his club career needs to take priority this month.
According to transfer expert Fabrizio Romano, Sevilla are still pushing to bring in the midfielder and want him to honour a 'verbal pact' between the two parties.
Romano claims that the La Liga outfit want to include a purchase option and a buyback clause in the loan deal, but it is unclear at this stage whether Man United will agree to it.
Ten Hag allegedly still believes that Hannibal could have a future at Old Trafford, with a successful loan spell in the second half of this season potentially leading to him fully kickstarting his career with the 20-time English champions.
Hannibal spent the 2022-23 campaign on loan at Birmingham City, representing the Blues on 41 occasions in all competitions, including 38 outings in the Championship.
The midfielder has been with Man United since 2019, making the move from Monaco, and he has represented the club on 13 occasions, scoring once.
The Red Devils have already sanctioned two loan exits this month, with Donny van de Beek moving to Eintracht Frankfurt, while Jadon Sancho has returned to Borussia Dortmund.
Dan Gore and Joe Hugill could also leave Old Trafford on loan before the end of the month.