The long-serving right-back will be departing Old Trafford this summer when his contract comes to an end.
The armband will be passed on as a result, with there several contenders in line to inherit the responsibility of being an on-field leader.
Paul Pogba, David de Gea, Chris Smalling and Ashley Young are among those to have covered for Valencia in recent times and Solskjaer admits that he has much to mull over.
The United boss said when quizzed on an impending captaincy call: “We’ll see who’s here for next season and I’ve got a couple of players in my head that could be captain.
“We’ve had Antonio, he’s going, we’ve had Ashley, we’ve had Paul, we’ve had David, Chris has been captain, so there are players here who can be captain on the pitch.
“We just need to decide who’s the club captain. Who’s going to be the voice in and around [the place].”
Exit talk continues to rage around Pogba and De Gea, with the former once again being linked with Real Madrid while the latter is yet to commit to a contract extension beyond 2020.
Both would expect to be the mix to skipper United should they still be around next season, with the qualities they bring to the United side fitting the mould that Solskjaer is looking for.
He added on what a Red Devils skipper needs to offer: “There’s a certain criteria.
“They have to be one of the, how do you say, cultural architects if I put it in a nice word. It’s someone you have to look up to, someone who’s got the right habits, standards and the personality to be that.”
Before a permanent successor to Valencia is appointed, United still have Premier League and Champions League contests to take in this season.
Victory over West Ham on Saturday will lift Solskjaer’s side back into top-four contention, while a must-win trip to Barcelona is set to be taken in on Tuesday as the Red Devils seek to overturn a one-goal deficit in Europe and book their place in the semi-finals.