The France international has struggled to find his best form since joining Everton from United in a £20m deal in January 2017 and he was jeered by Toffees fans against Crystal Palace earlier this year.
However, Schneiderlin has been impressive of late and received a standing ovation on Monday night when he was substituted due to injury on 52 minutes as Everton beat Newcastle 1-0 at Goodison Park.
Everton boss Sam Allardyce has backed Schneiderlin to kick on from recent performances and get back to his best.
"Sooner or later he has to find himself from where he used to be," said Allardyce.
"Sometimes it takes a while to find yourself after, I think, probably a disappointing move that didn't work at United.
"For the first time you find yourself in the squad not being involved very, very much indeed. Then you come to Everton and try and reinvent your career and show what you can do again. Sometimes it takes a bit of time.”
Allardyce believes that Schneiderlin needs to perform well every week in order to win the fans over on a regular basis.
He added: "There needs to be a bit more consistency. Morgan, if he continues to play like that and show that consistent level of form that he's shown in the past, particularly at Southampton, we will all get better as a team with him.
"Fans will always like to see you show your best and show commitment. They will always support you.”
Everton have suffered a disappointing season after spending over £120 million last summer before Allardyce replaced Ronald Koeman as manager, leading the team to a current position of eighth in the Premier League.
"Obviously the whole team suffered a lack of confidence at the start of the season,” said Allardyce. “Everybody's finally going in the right direction and ebbing back towards more and more confidence. I think the confidence is going the right way.”