United have a number of options in midfield and on Tuesday, Solskjaer played Donny van de Beek in a deeper role alongside Fred and behind Bruno Fernandes.
The Dutchman looked at home completing 56 passes, recovering the ball three times and winning three of his duels.
And he is now pushing to make his first Premier League start at the St Mary's with Pogba and McTominay unlikely to be fit to play and Nemanja Matic out of favour.
Solskjaer will also check on the fitness of Victor Lindelof, Aaron Wan-Bissaka and Marcus Rashford, who picked up knocks in the 4-1 win over Istanbul Basaksehir.
Luke Shaw, Jesse Lingard and Phil Jones are unavailable.
“Scott and Paul, they didn't train this morning,” Solskjaer said. “They were not on the grass so they are very unlikely for the weekend.
"Marcus, Victor and Aaron, they came through the session today, so hopefully they should be okay, [if] still not 100 per cent.
“Luke has just started his rehab out on the grass, he's not with the team yet.
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"Jesse's back from his isolation period so he's come back with the group and had a couple of days' training.
"Apart from that, Phil Jones is still out until probably after Christmas some time.”