Pogba has not been available for selection since suffering a thigh injury in the 3-3 draw with Everton at the start of last month.
Solskjaer said that Pogba would not return until March at the earliest, but the 27-year-old was ruled out of Wednesday's trip to Crystal Palace.
“Paul is still not ready for us,” Solskjaer said at his pre-match press conference.
“He's feeling better, he's not been training with the team yet so he's definitely not travelling down to London.”
When asked whether United fans will see Pogba return before the internationals, Solskjaer said: "I hope we will, definitely, and he’s very positive. He’s working really hard.
"He knows when he gets back we haven’t got two or three games to play him into form so he’s working hard on his fitness and when you’ve got the quality of Paul, fitness is the main thing.
"Mentality wise ... you know when the sun is out in Manchester there’s nothing to complain about."
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