De Gea sustained a groin injury during Spain’s 1-1 draw against Sweden on Tuesday night and will not recover in time.
The shot-stopper fell to the ground in pain after taking a goal-kick during the international fixture and was swiftly taken off.
“He had pain in the abductor muscle but he received treatment at half-time and wanted to keep playing,” Spain head coach Robert Moreno said.
The 28-year-old will undergo scans on Thursday to discover the extent of the injury.
It is the first injury De Gea has suffered in over two years and comes at an untimely period in Solskjaer’s reign.
The French midfielder sustained an ankle injury in early September and was rushed back into action too early, aggravating the knock.
He played 90 minutes against Rochdale and Arsenal at the end of the month but has not featured in the club’s last two fixtures.
Long-term absentees Eric Bailly and Timothy Fosu-Mensah will miss out against Liverpool but there still remain questions marks over Anthony Martial, Aaron Wan-Bissaka, Jesse Lingard, Mason Greenwood, Phil Jones and Diogo Dalot.
Pogba has been difficult to replace given United’s lack of options in midfield, with Nemanja Matic and Fred the main candidates.
Matic cannot get forward like Pogba and there are concerns over his mobility while the jury is still out of Fred’s best role.
Sergio Romero should come in for De Gea between the sticks, with the Argentine boasting a good record at United.
Romero has kept six clean sheets in seven Premier League appearances and United, in general, peculiarly have a better record without De Gea.
With the Spaniard, United concede on average one goal per game and take home 1.9 points; without De Gea, United concede on average 0.8 goals per game and collect 2.2 points.