Valencia wore the armband for much of last season but officially took on the role on a permanent basis when Michael Carrick retired to move into coaching.
The Ecuadorian has struggled for form and fitness this term, amid rumours of a fall-out with previous United boss Jose Mourinho, and has not featured in Solskjaer's two games to date as he fights to return to peak condition.
However, the Norwegian head coach has backed the veteran defender to win back his place in the team, while stating that he will retain the captain's armband for the foreseeable future.
"He's the captain. When he's properly fit and playing he'll wear the armband," said Solskjaer.
"He's going through a couple of tough sessions now to get him ready for the tough period coming up. There aren't many better right-backs going forward with his abilities."
Solskjaer has made a stunning start to his interim spell at Old Trafford with a 5-1 thrashing of Cardiff City, followed up with a convincing 3-1 defeat of Huddersfield Town on Boxing Day.
United's next test comes at home to Bournemouth on Sunday and the Norwegian is hoping to maintain the feel-good factor.
He added: "Whenever you win games everyone is happy. So let's keep that run going.
"We've got to focus on our performance against Bournemouth and getting three points there.
"These two games, yes, it's been fantastic... [we need to] keep that momentum going against Bournemouth. When you lose a game I don't think you'll see many smiles about."