The young Frenchman has picked up an ankle injury and is not expected to feature for the Red Devils for the remainder of this term, joining the Brazilian on the sidelines
French youngster Pogba picked up an ankle injury during a reserve match on Monday and will spend the remaining games on the sidelines, while Anderson has failed to make a recovery from a hamstring injury.
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"Ashley Young got a knock in the second half [against official Aston Villa] but I'm hoping he's okay," he told the club's website.
"The only injury we received is Paul Pogba, who got ankle damage in the Reserves on Monday. We think he's out for the season now."
Pogba's future at the club has been the subject of intense discussion in recent weeks with the teenager yet to agree a new deal at Old Trafford and heavily linked with a summer move to Juventus.
Meanwhile, Brazil international Anderson picked up his hamstring injury in March and was originally expected to be able to play some part in United's title run-in, but Sir Alex now believes this is unlikely.
"I don't think he'll play again this season," he added.
"There are only four games left and it will be difficult for him."