Maguire has only been at Old Trafford for a few months, but has been donning the armband for the last month in the absence of Ashley Young.
However, with Young leaving for Serie A giants Inter Milan, Maguire has taken over the armband on a permanent basis.
"He (Young) is 35 in the summer and if he gets a two-year contract somewhere it's up to him to take that," Solskjaer said, as per Sky Sports News.
"We weren't ready to offer that. He's been a good servant for the club, he's been captain, he's won trophies. But we've got players coming through.
"Harry has been wearing the captain's armband and he will keep wearing it. He's come in and been a leader in the group. I've been impressed by his leadership skills.
"Everything about him tells me he's a leader. He's part of a group that we've had that have been leading this young group."