The 27-year-old has remained loyal to the Bundesliga side, but has now suggested he will leave the club by the age of 30.
Leipzig has a policy of keeping the squad young and have no plans of moving away from that policy in coming seasons.
Forsberg has been linked with the likes of Manchester United, Arsenal and Roma recently.
The Swede told RBLive: “The best years are coming for me now. That’s why I’m glad I can now fully attack again.
“Whether I stay here until I’m 30, we’ll see. I think the club does not want 30-year-olds here. But I’m like a fine red wine, getting better with age.”