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.
"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.