Provided he stays fit and gets some confidence early he could be a fantastic option down the middle.
You have far more faith in Alexis than Solskjaer does, if his team selections are any indication of his thinking. If you look at what happened towards the end of last season, Sanchez appeared in good form during his sub appearance against Barcelona, then was an unused sub in the heavy defeat against Everton, got 7 mins in the defeat against Man City, 25 mins in the draw against Chelsea, then started against Huddersfield.
During the early part of the season, Sanchez will be reliant on injuries to other players simply to make the bench in the PL. Once the Europa League has started, assuming he is still here, he should get some playing time and could force his way into Solskjaer's thinking for the PL.
The nature of professional football is that some players get extended runs in the team to find their form, to show what they can contribute, while others have to perform at a high level when given a rare opportunity, just to stay in contention. Rooney under LVG, Zlatan and then Lukaku for Mourinho, most recently Rashford under Solskjaer, all started match after match, even when completely out of form. Sanchez got the benefit of the doubt under Mourinho until early October.
I suspect Sanchez views himself as a starter rather than a squad player. At Arsenal he started almost every match for which he was fit. Going back to his time at Barcelona, it was more of a mix of starts and sub appearances. If he doesn't leave in the next few weeks, I would have thought that a departure in January, most probably on loan, is more likely than him fighting his way back into United's PL team.
If he is prepared to wait for his opportunity then I would imagine he'd get one eventually, if only for a couple of games while other players are missing, then it would be up to him to impress.