British media have reported that Albion tabled an offer in the region of 13 million pounds for Schneiderlin, who has played only 11 minutes of Premier League football for United this season under Mourinho.
Asked later at a news conference if Schneiderlin wanted to leave, Mourinho said: "Yes. He opened his heart a couple of times. He is a great professional, a fantastic boy.
"If he is playing regularly, I have a right to say 'no way'. If he is not playing regularly, I have no right to say 'you are not going anywhere'.
"If the offer is right and our board thinks the offer is good, I would not stop him going."
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Albion could find themselves competing with other clubs for Schneiderlin, who cost 25 million pounds when United bought him from Southampton in 2015. Everton have also been mentioned in the British media as potential suitors.
West Brom hope to strengthen their squad, building on their impressive form as they lie eighth in the Premier League after 17 games.
"We have made bids for about five players. Doing business with people should be done directly with them. We aren't going to try and do everything in one window. It might take a couple of windows to get the quality in that we want," Pulis said.
West Brom, who lost to Manchester United on Saturday, will hope to get back to winning ways when they travel to fourth-placed Arsenal on Monday.
(Reporting by Shravanth Vijayakumar in Bengaluru and Ian Chadband)
