Solskjaer is under increased pressure at Old Trafford, following a week in which saw the team draw 0-0 with AZ Alkmaar in the Europa League and lose 1-0 to Newcastle United.
The loss at St James’ Park, has left United with just nine points from eight games in the Premier League.
After taking over from Jose Mourinho last December, the Norwegian told Woodward that he felt as many as nine players at United needed to be replaced.
United spent around £150million this summer on signing Harry Maguire, Daniel James and Aaron Wan-Bissaka.
Solskjaer also allowed six first-team players to leave Old Trafford as Romelu Lukaku, Alexis Sanchez, Antonio Valencia, Ander Herrera, Matteo Darmian and Chris Smalling departed. The 46-year-old also gave the green light for Marouane Fellaini to leave for the Chinese Super League in February.