The 28-year-old has rejected a new contract offer from United, with him struggling for game time despite an incredible loan spell with West Ham United last season, and also despite being promised more minutes by Ole Gunnar Solskjaer.
However, the source claims that the Toffees have a major advantage in the deal, as Lingard would prefer to remain in the north-west, avoiding the need the relocate.
The report adds that geographical reasons were crucial to him remaining at Old Trafford during the summer, especially when West Ham were pushing so hard to sign him permanently.
With Everton being restricted by Financial Fair Play regulations, eyeing a move for Lingard, who is out of contract in the summer, might seem as an ideal transfer for all parties, with United wanting to avoid losing him for free, while Everton will be able to get him on a cheaper deal.
Additionally, Everton could also sign Lingard on loan and then make the deal permanent in the summer.
Rafael Benitez's priority right now is to sign an energetic attacking midfielder that has the abilities to score, and also create goals.
Lingard would have hoped to re-establish himself as an Old Trafford favourite, but Solskjaer has refrained from starting him in a Premier League or UEFA Champions League game so far this season.
While Lingard has been starved of minutes this season, he has proven to be a game-changer in big games for United, scoring twice despite getting just 146 minutes in all competitions.