The Bayern stalwart's contract expires at the end of the season and there had been speculation the 34-year-old could move on.
But Ribery revealed a strong desire to remain at the club he joined from Marseille back in 2007.
"My aim is to stay at Bayern Munich for as long as possible," he said.
Speaking about a successful return to Bundesliga action at the BayArena, the winger added: "Normally I provide a lot of assists and do a lot of dribbling – but it's always great when you score a goal.
"You know when you play in Leverkusen it is always a difficult game. But after working hard in Qatar [during a mid-season training camp] we played well – although we managed to win 3-1 it was tricky as Leverkusen put us under a lot of pressure.
"I am pleased to be fit and healthy. I'm having fun with the team, enjoying playing and training as well."
Jupp Heynckes' side sit 14 points clear at the top of the table in pursuit of a sixth successive title.