The Chile worldwide did not travel with the squad to the south coast, BBC Sport reports.
United were expected to be relatively quiet in the current window, but have unexpectedly launched a move for Arsenal's Alexis Sanchez in a bid to snatch him from under the noses of Manchester rivals, Man City.
"I think it's a good investment because we are talking about a top player and I'm hearing that the amount is around £20m".
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Reports have also emerged that Mourinho will attempt to sign Arsenal forward Alexis Sanchez, who is also out of contract in the summer.
Neighbours Manchester City are said to have a verbal agreement in place which would explain why they haven't been in a rush to meet Arsenal's alleged valuation of £40 million.
City were ready to pay £20 million to sign the player this month, however they've dropped their interest with United ready to offer £25 million, and possibly Henrikh Mkhitaryan in part-exchange.
"But if there is a fantastic opportunity on the table, you fight for that fantastic opportunity".
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But nothing is quite so straightforward during transfer season and Manchester United threw a spanner in the works by making a late swoop for the Chilean. City, responding to this, have ended their pursuit and it seems Manchester United are now the only interested team. Sanchez wants to be around players who are as good as him, maybe even some that he believes are better than him.
The Potters away form will be a concern for the players and fans alike, with no wins in their last seven on the road and Stoke sat in the bottom three going into the clash at Old Trafford.
United boss Jose Mourinho said Sanchez is a "phenomenal player" on Friday. However, he and his agent are understandably considering United's offer, and any deal could depend on Arsenal securing a replacement, with Bordeaux's Brazilian forward Malcom said to be their main target.
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