The 27-year-old France international was signed from Southampton for £25 million in 2015, but has become a peripheral figure under United manager Jose Mourinho, making only eight appearances this season.
Sky Sports reported that the fee could rise to £24 million with add-ons.
After United’s 2-0 League Cup semi-final, first leg win over Hull City at old Trafford, manager Jose Mourinho told Sky Sports: “Before the match I was informed by Mr (Ed) Woodward (the club’s executive vice-chairman) that the situation is to close, so Morgan is more than probably going to Everton.
“I am sad and happy, sad because I like him and he could be an option for us, happy because this is what he wants, to play every game and be important in the team.”
The news comes days after Everton manager Ronald Koeman urged the club’s board to back him in the transfer market after Saturday’s FA Cup exit at home to Leicester City.
