"I feel like I want to continue," he told the Register. "But the circumstances kind of have to be right in a way that I feel comfortable, my family feels comfortable and I'm not going to drag my family and move the kids and do something just for a year or go into a rebuilding kind of (situation).
"But I do feel that I can put the work in the summertime and I have the push to do it again."
The 37-year-old's two-year contract is up after this season and it will be a question of whether the Ducks want to keep him though his offensive numbers are in decline.
The team, however, values Koivu's ability in other areas, such as winning faceoffs in key situations, killing penalties and for his overall competitive nature and professionalism.
The veteran player will also need to accept a lesser role as a checking-line forward and a decrease in pay from the $2.5 million per season he makes on his current deal.
"A year difference sometimes means a lot," Ducks coach Bruce Boudreau said. "Sometimes it means a little. He works hard every night. He doesn't take nights off. He's an extremely smart player. Another guy that can play for a while, I think."
In 72 games with the Ducks this season, Koivu has posted 11 goals and 26 assist for 37 points.
Meanwhile, with the possibility that Koivu will return with the Ducks, the same cannot be said for enforcer George Parros, who has recently been a healthy scratch as his role has been diminished.
If the 32-year-old is unable to adapt to the latest changes facing NHL enforcers, he could find himself not only jobless in Anaheim, but perhaps unable to find another team in the league to sign with.