West Brom have allegedly made three other bids for the Frenchman last week, but were all rejected by Jose Mourinho.
He is also said to be wanted by Premier League rivals Everton and could be included in a deal which would also see Memphis Depay leave Old Trafford.
Tony Pulis is making Schneiderlin his number one target for the transfer window and would be smashing the club’s record fee which was set when they paid Tottenham £13 million for Nacer Chadli in the summer.
Jose Mourinho is keen to cut Schneiderlin out of the squad before the transfer window closes, but won’t budge on a price unless he’s happy.
United paid Southampton £25 million for him just 18 months ago, but Mourinho could be in for some profit if both clubs decide to go into a bidding war.
The club have been terrible at selling players in recent years and it seems Mourinho wants to showcase his intent in the transfer market this month as he looks to make as much as he can off the out-going players.