The Toffees are the latest team to show an interest in the France international after Jose Mourinho said that the midfielder was free to leave Old Trafford.
West Brom were thought to be interested in Schneiderlin and recently had an £18m offer rejected, as it is reported that United want to recoup the £24m they paid Southampton for the player two-and-a-half years ago.
'Sky Sports' is reporting that Everton are in preliminary discussions with the Red Devils over the signing of the 27-year-old and say that Ronald Koeman's side have had an opening bid of £19m rejected.
The Toffees are in need of a central midfielders as arguably their best midfielder, Idrissa Gueye, will leave the club for a month to play for Senegal in the African Cup of Nations, while fellow midfielder James McCarthy has struggled with injuries this season.
This means that Everton have turned their attention to Schneiderlin, but the Frenchman, who has made just three substitute appearances this season, will not be available on the cheap.