Cavani sealed a free move to Old Trafford on transfer deadline day after leaving Paris St-Germain in the summer, but he is yet to make his first United appearance.
The 33-year-old was forced to undergo a two-week quarantine period upon arrival in Manchester, meaning he only trained with his new team-mates for the first time on Monday.
Nevertheless, Solskjaer has confirmed Cavani is in line to make his Red Devils bow in tonight’s clash with Chelsea.
“Of course where he's been away from football for so long, he needed a pre-season,” the United boss said.
“He's naturally fit and he's been looking after himself. He had two weeks in quarantine but we did provide him with all the facilities - the gym and a treadmill - and he posted (online) a few running sessions that he did.
“There is your foundation. Now when he comes in with us he's getting more football and more training sessions individualised so he feels more ready to train with the team and then play with the team.
“He's been very meticulous and very methodical in his training and his preparation. He didn't feel ready for the PSG game because it was too early for him.
“He hadn't done enough sharpness work, but he's managed to do that this week and let's see if that means he's ready for the Chelsea game - I'm hopeful.”
Solskjaer could be without a host of key players at Old Trafford this evening, with Mason Greenwood and Harry Maguire both doubts to feature.
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Axel Tuanzebe could keep his place in the back three after a stunning performance away at PSG in the week, while Alex Telles could make his first Premier League start for United at left-back.
Anthony Martial is also unavailable while serving the second of his three-game suspension.