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The 34-year-old Uruguayan scored United's second goal with an excellent diving header in Sunday's come-from-behind victory and had an earlier effort controversially ruled out.
Cavani arrived at Old Trafford as a free agent last October on a deal until the end of the campaign, with the option of a further year.
Unlike most extension clauses, it has to be agreed by both parties before it can be triggered and there is speculation that Cavani could move to Argentine giants Boca Juniors.
"Fantastic performance, we are awaiting his decision if he wants to stay or wants to move on," said Solskjaer.
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"A performance like today, we as a club have missed for a few years, we have not had that number nine for a long, long spell.
"Edinson has been working so hard to get fit and we can see the boys played to his strengths as well.
"We have had open and honest meetings and it's no secret we want to keep him."
Cavani took his tally to eight goals in 29 appearances for the club in a season marred by injuries.
He also served a three-match Football Association ban for using a racial term in a social media post and apologised for any unintentional offence caused.
However, Solskjaer says it has been the inability to travel and see family or for them to visit due to the coronavirus pandemic which has upset Cavani.
"I don't think it is any secret that this has been a difficult year for everyone," he said.
"With the pandemic, it has not been possible to have friends over, you can't have family over without quarantine.
"He has not been able to experience the fantastic culture of Manchester and England and he is contemplating and thinking long and hard about what he wants to do.
"I understand. He knows what we want, I want him at Old Trafford in front of a full Stretford End scoring a header like today. Let's wait and see."
pi/jc