Sanchez was sent to Inter at the start of the season after a woeful first 18 months at Old Trafford, as he scored just three Premier League goals in 32 matches.
The Chile international had arrived to much fanfare from Arsenal in a swap deal involving Henrikh Mkhitaryan in January 2018, but he failed to meet expectations.
He is yet to make much of an impact at Inter either, making just five Serie A appearances – though injuries have played a part.
Reports had suggested Inter players were keen on Sanchez staying regardless, but Solskjaer is seemingly expecting the forward to return to Old Trafford at the end of the season, as he appeared resigned to not bringing in any reinforcements this month.
After being asked about United's hopes of signing reported target Bruno Fernandes, Solskjaer – who was speaking ahead of the EFL Cup semi-final second leg with Manchester City – 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. I haven't got anything to say now, my mind is on the game.
"We've got players here that we're working hard to get back as well, and if there is something out there, then the club is pursuing that and it's difficult.
"I can't remember how many good ones [signings] we've brought in with good deals in January.
"Henrik [Larsson] was good, Nemanja [Vidic] and Patrice [Evra], I'm talking about it's hard, very hard, the clubs don't want to lose their best players.
"And then Alexis will come back in the summer and will prove us all wrong."
One player heavily linked with leaving the club is Marcos Rojo, who had emerged as a target for his former team Estudiantes in Argentina – their sporting director and one-time United midfielder Juan Sebastian Veron previously confirming the interest.
But Solskjaer has no plans to part with the Argentina international.
"I wouldn't think so," was Solskjaer's response when asked if Rojo could leave this month. "Marcos has been injured and is working to get back and get fit again."