Cavani’s new contract ends at the end of this season, with a one-year extension clause if all parties consent.
According to reports in South America, the Uruguay striker is interested in joining Boca Juniors because he wants to get closer to his family.
But after Cavani’s excellent display against AS Roma in a 6-2 Europa League semi-final first-leg win on Thursday, Solskjaer hopes the striker stays.
“Edinson was out for seven months and not playing football for a very long time before he came to us,” Solskjaer said.
“He’s had a couple of injuries and has worked really hard to show his quality.”