Cavani, who joined the Red Devils on a free transfer this month after his Paris St Germain contract expired last season, had to self-isolate for 14 days on arrival in the United Kingdom.
The 33-year-old was ruled out of the 4-1 league victory over Newcastle United and missed the 2-1 Champions League win at his former club on Tuesday, but has worked on his fitness levels to come into contention for his first game since March.
"Of course, he's been away from football for so long, he needed a pre-season," Solskjaer told reporters on Friday.
"He's naturally fit and he's been looking after himself... now he's getting more training sessions individualised so he feels ready to train with the team and play with the team.
"He's been very meticulous and methodical in his training and his preparation. He didn't feel ready for the PSG game... he hadn't done enough sharpness work, but he's managed to do that this week. Let's see if that means he's ready for Chelsea."
Solskjaer's side are 15th in the Premier League table with six points from four matches, while Chelsea are ninth with eight points but have played one game more.
