The former PSG and Napoli striker joined United on a free transfer and has already made three substitute appearances against Chelsea, Leipzig and Arsenal.
Cavani could contribute to United’s attack in Europe this week with the away test against Istanbul Basaksehir.
And Solskjaer is excited by the progress made by the 33-year-old, who is the 18th highest scorer in the competition’s history with 35 goals in 63 games.
“He’s generally a fit man anyway and he’s getting his sharpness in training and he’s got some substitute appearances now,” Solskjaer said ahead of the Red Devils’ trip to Turkey.
“We haven’t managed to get him long enough yet to make a big impact but he’s looking sharper and sharper in training so it won’t be long.”
Solskjaer is also eager to reintegrate Martial after missing the Frenchman due to suspension in the 1-0 defeat against Arsenal on Sunday.
“Anthony has been important for us last season and in the time I’ve been here. So, of course, to have him back is a boost,” said Solskjaer.
“It gives us more options for up front and on either side, and we’ll look forward to seeing the best of Anthony.
“I thought towards the end of the Leipzig game you could see his sharpness getting there and he was really positive and bright which is good.”