The England defender picked up a knock in the 3-2 victory over Brighton last Saturday and did not feature in the EFL Cup win over the same opponents on Wednesday night.
United host Spurs on Sunday afternoon at Old Trafford and Solskjer is confident his captain will have recovered in time for the big game.
‘Harry had a knock after the league game, holding his ankle, he should be okay, we’re okay no more injuries from the cup game,’ said the Norwegian.
The Red Devils boss did not provide an update on Bruno Fernandes, who was reportedly struggling with a thigh injury earlier in the week and also sat out the Carabao Cup win over the Seagulls.
The Portuguese midfielder missed training due to the complaint but is expected to be fit for the meeting with Spurs.
Phil Jones and Axel Tuanzebe remain sidelined for United and will not be involved.
Solskjaer says he has spoken to Southgate about the decision, respects it, and will appreciate the time to spend training with Greenwood.
‘Mason is one of the top strikers of the future for England and I’m sure he’s gonna play many games for England,’ said the United manager.
‘This now has been a learning curve for him, Mason has to reflect where he’s at what he needs to do how to get where he wants to get.
‘I had a very nice chat with Gareth abut our England players and as I said earlier on games at this point it’s important for players to get some minutes. We’ll get loads of training in for Mason, I respect Gareth’s decision.’
United and Spurs meet at Old Trafford at 4.30pm on Sunday.