In July 2015 Schneiderlin joined the Red Devils for £25m from Southampton.
This season he has only played 11 minutes of Premier League football.
Other interested one is Everton, managed by former Saints boss Ronald Koeman.
West Brom manager Tony Pulis said:
“I don’t want to say any more than confirm our bid. We have to be fair to Manchester United and the player.”
In August, West Brom reportedly paid £13m to sign Tottenham midfielder Nacer Chadli, so the offer for Schneiderlin seems to be close to the club record fee.