Jones has 24 caps for England and is an experienced Premier League defender. Allardyce gave Jones his debut at Blackburn Rovers and he is now keen to be reunited with the defender at Goodison Park should he remain in charge next season.
The 26-year-old, who reportedly earns £50k-per-week, has made 21 Premier League appearances this season, and has not played since the 1-0 defeat by Newcastle United on February 11.
Jose Mourinho has plenty of central defensive options, with the likes of Chris Smalling, Victor Lindelof, Eric Bailly and Marcos Rojo all fighting for places.
The report claims that Mourinho is expected to seek reinforcements this summer and may have to sell a few players to balance the books.
Jones’s contract at Manchester United expires at the end of next season, and United must decide whether to sell him now or offer him a new deal.
Everton need to prioritise a defensive overhaul this summer and Jones will be a fantastic addition to the squad.
Michael Keane and Ashley Williams have largely struggled while Phil Jagielka is nearing the end of his career.