Sanchez was allowed to join Internazionale on loan at the start of this season after a disappointing 18 months following his arrival in January 2018.
The Chilean has only made seven appearances for Inter since joining, scoring just one goal, and is likely to return to Old Trafford at the end of the season.
Despite having a lack of options up front following Marcus Rashford’s back injury, United are unable to recall Sanchez from his loan spell early.
While Solskjaer was discussing United’s history of January signings, Sanchez’s name was mentioned as one who had failed to live up to expectations.
“Alexis will come back in the summer and will prove you all wrong,” the United manager replied.
On the potential for January signings this month and United’s pursuit of Bruno Fernandes, Solskjaer said: “I haven’t got any updates for you on transfers.
“I think it was a waste [of a question], I gave you the option [of not asking it]. I haven’t got anything to say now, my mind is on the game.
“We’ve got players here we’re working hard to get back and if there is something out there the club is pursuing that and it’s difficult.
“I can’t remember how many good ones we’ve brought in and good deals in January.
“Henrik [Larsson] was good. Nemanja [Matic] and Patrice [Evra]. I’m talking about it’s hard, very hard. The clubs don’t want to lose their best players.”
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