The Belgian made over 200 appearances for the Merseyside club before leaving in 2019 to join Brugge, where he has since become the number one keeper.
According to Belgian outlet Het Laaset Nieuws, United manager Erik ten Hag is seriously considering a move for the 34-year-old shot stopper.
United's current number one David de Gea is out of contract next summer and while the club are expected to renew his deal, the Dutch manager may still opt for another option.
The Red Devils have four goalkeepers on their books, including Martin Dubravka who arrived this summer on a loan deal from Newcastle United but is yet to make an appearance.
Additionally, United have Tom Heaton who himself has only featured once since re-joining the club for a second spell in 2021.
There is also Dean Henderson who is on loan at Nottingham Forest, but it is unclear what Ten Hag's preference is for the England international going forward.
Mignolet has kept 11 clean sheets in 18 games this season and is set to go to the World Cup with Belgium where he will be backup to Real Madrid's Thibaut Courtois.