However, his form has dipped since he was sent off in the first leg of United's Champions League last-16 tie against Paris Saint-Germain in February, with no goals and just one assist in his past eight matches.
"We'll see who's here for next season and I've got a couple of players in my head that could be captain", said Solskjaer.
"It's going to be survival of the fittest or survival of the best", Solskjaer said ahead of West Ham's visit to Old Trafford today.
"We had players on the bench on Wednesday night such as Jesse [Lingard] and Anthony [Martial] who normally start".
Pogba sparked intense speculation about his future last month when suggesting Madrid were "a dream club for every player" despite declaring himself happy at Old Trafford. That's how ruthless we have to be in the end. We are Manchester United, even if they are Barcelona - we are Manchester United, and we play in the Champions League just like they do.More news: Jurgen Klopp wins Premier League manager of the month award for March
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"We're under no illusion it's going to be hard work and there will be some tough decisions made by me, Mick [Phelan, the assistant manager] and the club".
"We have a certain standard here", Solskjaer added.
"The chances that we get, we have to put them in".
"That was important to me and then as I've said, he allowed me to go back to Argentina to be with my family a while, as we didn't have any fixtures". For me the most important reason for any inconsistency is the amount of players we couldn't use.
Luke Shaw and Ashley Young are suspended for the game but Solskjær has a few more options at full-back to choose from this weekend, with Matteo Darmian and Marcos Rojo available after injury, though midfielder Nemanja Matic is not quite ready to return.
"But now it's about West Ham and focusing on a good performance to give us three points". Meanwhile, West Ham is in 11th place with a record of 12-6-15 and 42 points.