Sources have told ESPN that Cavani is "closer than ever" to agreeing a deal with Boca rather than extending his stay at Old Trafford into a second season.
Speaking ahead of the trip to Tottenham on Sunday, Solskjaer hinted that the decision is in Cavani's hands and that the 34-year-old was yet to inform the club of his plans.
"I've kept in touch with Edi of course," Solskjaer said. "We keep an open dialogue and he's still unsure what he wants to do next season, which I find fine. It's not been an easy year either for him or the rest of the world, this season, so he still wants time to make his mind up.
"I'm very sure we will get the good version of Edinson for the rest of the season. He knows this is the business end of season.
"He's been so positive in and around the place, he's been great to have."
United's trip to Tottenham will be the first time they have faced Jose Mourinho's side since the 6-1 defeat at Old Trafford in October.
They have battled back to lift themselves up to second in the Premier League table with eight games to go but Solskjaer said the result still hurts six months on.
"I think the players will remember that game with a lot of pain and their pride has been hurt, our professional pride has been hurt," he added.
"The way and the manner we lost is not ourselves and we know that. We gave ourselves a difficult game by having 10 men.
"Preseason was short and we weren't up to the standard required, but we were so poor and I'm pretty sure we'll see some players wanting to prove that we're better than that."
Victory on Sunday would further cement United's place in the top four and damage Tottenham's hopes of qualifying for next season's Champions League.
After guiding United to a second-place finish in 2018, Mourinho said it was an achievement to rank alongside his Premier League and Champions League wins but Solskjaer was clear that it will not be good enough for him.
"We should never settle for second place at Man United and we will never settle for second place, I think that's the point here," he said.
"We have seen the heights and we know what this club is capable of. I've been here for a little while myself and it's taken time for us to be in this position. Hopefully we can be better next season because this is below our ambitions."