The Uruguayan centre forward hints that he could stay at the San Paolo beyond the summer, with the Partenopei likely to play in Europe's top competition next season
The Uruguayan forward has long been linked with a move away from the San Paolo, with both Manchester City and Chelsea revealed by Goal.com as suitors.
However, with the Partenopei sitting second in Serie A, the former Palermo man is hoping to play in Europe's top competition once more.
"It would certainly be a pleasure to play for Napoli in the Champions league again," the 26-year-old told reporters.
"I can only say that I will give everything until the last second for this shirt."
Napoli drew 1-1 with 10-man AC Milan on Sunday and Cavani remarked that he is disappointed not to have won the game but still feels that his side can win the title this season.
"We tried to win a hard-fought match. We're a little sorry. It was important to beat Milan, who in my opinion did very well with 10 men," he observed.
"Second place depends on us, it's up to us. Actually, looking at the team above us, the championship is not even decided. We will do everything we can."
Napoli sit eight points behind Juventus in the table having played a game more.