The defender skippered the Red Devils on Sunday and his manager says he could earn the role permanently
United cruised to a comfortable victory at Old Trafford against Brighton, with the visitors arguably lucky to avoid losing by a crushing scoreline.
Maguire led the team out as captain and put in a generally commanding display at the back, as he continues to look a solid acquisition following his reported £80million switch from Leicester City.
The centre-back was captain in the absence of Ashley Young, though Solskjaer suggested Maguire could potentially get even more familiar with the position in years to come.
“Harry has come in and been excellent in the dressing room and on the pitch,” Solskjaer told reporters.
“He can be a long-term captain.”
The one dampener on United’s win was a late ankle injury suffered by Scott McTominay, as he appeared to roll his foot and was left in agony.
While he was able to hobble off the pitch aided by United’s medical staff, after the match he was carried away on a stretcher.
But Solskjaer was unable to offer much of an update on his condition aside from being set for scans on Monday.
“He went over on his ankle,” said Solskjaer. “It’s a painful one sometimes.
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“I’ve had one, I was out for eight weeks but then again sometimes you have one and you’re back in two weeks. I don’t know.
“He’s in for a scan tomorrow and then we’ll have to see, with the ice there. But it looked painful – Scotty’s not one for rolling around.
“He didn’t really roll around, because that’s probably the sign he’s injured. All the players that keep rolling aren’t injured.”