The 27-year-old France international was signed from Southampton for 25 million pounds in 2015, but has become a peripheral figure under United manager Jose Mourinho, making only eight appearances this season.
The fee could rise to 24 million pounds 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 reporters: “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.
Everton let slip a one-goal lead at Goodison Park with Nigerian striker Ahmed Musa’s second-half double enough to condemn the Merseyside club to a 2-1 third round defeat and the likelihood of another season without silverware.
Schneiderlin was not part of the United squad to play Hull City in their League Cup semi-final first leg on Tuesday.