France international Schneiderlin, 27, was signed for United by Louis van Gaal for £25m from Southampton in July 2015.
He has played 47 times for the club but has only featured eight times under Jose Mourinho this season, including three Premier League appearances.
Everton, meanwhile, have agreed to loan striker Oumar Niasse, 26, to Hull, with personal terms still to be agreed.
The Senegal international signed for £13.5m from Lokomotiv Moscow in February 2016 but has played only seven times for the Toffees.
Following United’s 2-0 win against Hull on Tuesday, Mourinho said: “Executive vice-chairman Ed Woodward informed me that the situation is close. 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.”