Manchester United are hopeful Aaron Wan-Bissaka and Daniel James will return for Sunday's derby but captain Harry Maguire is 'touch and go' to make it.
Wan-Bissaka did not travel with the squad to Derby County for United's 3-0 FA Cup fifth round stroll due to a back injury, and James missed his second game running with a knock.
Maguire was also not included in the travelling squad after he sustained an ankle injury in training and has started every Premier League game this season. Paul Pogba (ankle) and Marcus Rashford (back) are still unavailable but Pogba is expected back in full training next week.
"I hope so but none of them have been training yet since the last game," Solskjaer said of Wan-Bissaka and James. "We've got to look at them Saturday probably, [Friday]'s the recovery day.
"It's touch and go [with Maguire] because he rolled his ankle and he twisted his ankle, but hopefully he'll recover quickly. I wasn't going to rest him today, so I didn't give him a day off birthday-wise! But I hope he'll be fit."
United are unbeaten in their last nine and kick-off against City on Sunday shortly after Chelsea play Everton at Stamford Bridge. Chelsea are still three points clear of United after dropping more points at Bournemouth last week, while Tottenham Hotspur lost their second successive league game to Wolves, now up to sixth.
Although United are striving to finish in the top four, they technically occupy a Champions League qualifying berth in fifth, pending City's appeal against their two-season ban from the Champions League. "We've just got to concentrate on ourselves," Solskjaer explained. "Keep improving and keep getting results.
"But I know it's going to be tight. Wolverhampton, they're definitely putting up a challenge as well. There's loads of teams that want to get this top four. We're one of them.
"We've just got to be able to handle and manage a squad well enough, rotate well enough. These next few games are important. If you can get six points against City and Tottenham now we've given ourselves a good chance."
Possible United XI vs City: De Gea, Wan-Bissaka, Lindelof, Maguire, Shaw, Matic, McTominay, Fred, Fernandes, James, Martial