Coutinho is on a season-long loan deal from LaLiga holders Barcelona, however, the Brazilian is yet to convince in Bavaria.
Since swapping Camp Nou for Allianz Arena, Coutinho has scored three goals in 18 appearances for Bayern.
"I feel really good," said Coutinho. "I'm planning to stay here for a year and focus on the here and now.
"But if everything fits, then I'd love to stay."
Coutinho came off the bench in Bayern's shock Bundesliga loss at home to Bayer Leverkusen on Saturday.
It was Hansi Flick's first defeat since replacing Niko Kovac as head coach until the end of the year.
"We understand his way of training and playing well," Coutinho added. "Things are going well because of that.
"Flick makes everyone feel important and we're happy, but we know there's a lot of work to do."
Bayern – fourth in the Bundesliga and four points adrift of leaders Borussia Monchengladbach – face the German pacesetters on Saturday.