Ashley Young has claimed the armband for much of the season – but with the England international set to turn 34 before the start of next season, Solskjaer is likely to look for a longer-term option, with Paul Pogba, David de Gea and Chris Smalling leading candidates.
“We'll see who's here for next season," said Solskjaer. “I've got a couple of players in my head that could be in the group of captaincy.
“We've had Antonio, he's going. We've had Ashley, we've had Paul and David. Chris (Smalling) has been captain.
“There are players here who can be captain on the pitch. We just need to decide who's going to be the voice in and around.
“There's always certain criteria. He has to be one of the 'cultural architects', to put it in a nice way.
“Someone you look up to, someone with the right habits and standards and the personality to be that."