The Frenchman made his return from injury in United’s 2-0 defeat to Watford before Christmas and managed an extra 45 minutes against Newcastle on Boxing Day.
However, he was left out of United’s squad for their 2-0 win against Burnley on Saturday, which Solskjaer claimed was down to the congested fixture list at this time of year.
United take on Arsenal at the Emirates on New Year’s Day and Pogba was seen entering the club’s training ground on Monday morning.
But the 26-year-old was not seen during a public 15-minute session, though there is a possibility that he joined the rest of the group once the media were forced to vacate.
Nevertheless, it’s a worry for Solskjaer that his star man is still feeling the effects of the foot injury that kept him sidelined for three months earlier this season.
Elsewhere, there was positive news in the return of Eric Bailly, who was making his return to training after five months out with a knee injury.
Arsenal trail United by seven points but can reduce the gap to four if they can manage a first win under new boss Mikel Arteta.
Two late goals from Chelsea at the Emirates on Sunday inflicted the first defeat of the Spaniard’s reign at the club but there were clear improvements in the Gunners’ play and attitude.