Cavani signed a one-year contract upon arrival at Old Trafford in October, with the option of extending for a further season, but is thought to be considering a return to his native South America this summer to be closer to his family.
Boca Juniors are among the clubs interested in the 34-year-old, who has scored seven goals in 28 appearances since joining United as a free agent.
The last of those goals came more than two months ago, however, in the 3-3 draw with Everton and Cavani has struggled for fitness since a promising start to his United career.
Solskjaer said last month that discussions are being held with the Uruguayan but the ball is in Cavani's court, and that remains the case.
“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 easy year either for him or the rest of the world, this season, so he still wants time to make his mind up."
Cavani replaced Marcus Rashford as a second-half substitute in United's 2-0 Europa League quarter-final win over Granada on Thursday night, having started Sunday's Premier League win over Brighton.
With Anthony Martial likely to miss the remainder of teh season through injury, Solskjaer is confident that he will be able to rely upon Cavani to return to form and lead the line.
“I’m very sure we will get the good version of Edinson for the rest of the season,” he said.
“He knows this is the business end of season, where we fight for the Europa League trophy and we can see the end line in the league.
“Only eight games left and you're thinking about where you're going to end up. He’s been so positive in and around the place, he's been great to have.
“He's been working hard now to get fit and we’ve got him. Now hopefully we can keep him fit for the next six or seven weeks."
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