He was expected to return to training this week, with United set to face Colchester United in the Carabao Cup at Old Trafford on Wednesday.
However, after attending his brother Florentin's wedding in France last week, he has now been hit with an illness that Solskjaer said will further delay his return to fitness:
"Of all things, he's now struck down with illness ,and he's been off for two or three days. That's not beneficial, and that's probably set him back quite a bit.
"As I've said so many times, Paul is a top player that we want to see playing his best football at Man United. We just need to get him match fit. He might be half an hour, 45, 60, 90 minutes—who knows—in the first game. We're working hard to get him back, but now he's ill."
Pogba, 26, has not played a minute for United since their 1-1 draw with Arsenal at Old Trafford on September 30.
A collapse in form from Chelsea, though, has put the top four within reach for sixth-place United, especially if they pick up some good results in the busy Christmas period:
The first three are all against sides in the bottom half of the table, while the struggling Gunners are 10th.
In seasons past, United would have been expected to take a minimum of nine points from that set of fixtures, but Solskjaer's current side tend to struggle most against teams they are expected to beat.
The return of Pogba could help the Manchester giants address that issue because, as Solskjaer said after Sunday's 1-1 draw with Everton, he has the ability to provide "one creative pass or idea" that can unlock an opposition.
He will also be slotting back into a midfield that is high on confidence due to the ongoing impressive form of Scott McTominay and Fred.