Rashford was replaced by Ashley Young in the 80th minute, and Maguire limped through the last few minutes of the game.
United have little turnaround time before the 12.30pm kick-off at the Vitality Stadium, but Solskjaer is confident Rashford and Maguire will be available.
“We’re playing football, it’s not basketball,” Solskjaer told MUTV when asked about the duo.
“Some of them are sore but you should be absolutely down on your knees, because it’s worth it.
“But they’re quick healers and hopefully they’ll be ready for Saturday.”
Rashford was one of two star performers Solskjaer picked out for praise after the EFL Cup victory.