Several players will be out of contract this summer and in 2021.
Those who are free agents in six months’ time will be allowed to sign pre-contract agreements with overseas clubs.
For those with 18 months left on their deals, United will quickly have to make a decision as to get them to sign new deals or try to offload them for the highest transfer fee.
After United’s 3-1 defeat to Man City in the first-leg of their Carabao Cup semi-final, Solskjaer said: “I think every player is playing for his future at the biggest clubs. You have to perform and you have got to do well.
“We all have different roles in it, at a different age you have got more influence behind the scenes as well to be one of the main characters.
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“Both on and off the pitch, everyone here has a lot to play for.”