The Spaniard came off at half time against Southampton in the Premier League on Sunday.
He suffered a blow to his knee, and it was feared he may miss one or two games.
But it appears De Gea is quickly back to full fitness and available for selection, while Edinson Cavani is also fit to play.
Solskjaer told reporters: "David trained well today so he's available for selection and Edinson is ready to play."
De Gea has maintained his spot as number one this season despite pressure from Dean Henderson.