The versatile midfielder has made 298 appearances for the Bavarians in his seven seasons at the club. He has won the Bundesliga title each year, as well as the 2020 Champions League.
Kimmich is generally regarded as one of European football's best players and has made 66 appearances for the German national side.
"That would be an interesting challenge. I don't know what will happen in a few years, we'll see."
The German added:
"I have a very good coach who is an advocate of attractive football. I have a lot of fun here, but somewhere in my head there is always this professional and personal challenge of one day reaching new horizons to discover."
Kimmich still has three years left on his current Bayern Munich contract, having contributed three goals and 12 assists in 39 appearances across the most recent campaign.
Bayern Munich star Joshua Kimmich claims Germany need to "show a little more humility" ahead of Qatar World Cup
Kimmich's former Bayern boss Hansi Flick is set to take his Germany side into a major tournament for the first time later this year. He had previously led the Bavarians to a historic treble in 2020.
Die Mannschaft will be aiming to improve upon their 2018 performance in Russia, where they were knocked out during the group stage.
The Germans will be aiming to become just the second side to win five World Cups. Kimmich feels that his nation will be one of the favourites for the title later this year.
He told So Foot:
"In Qatar, anyway, the level will be very high. Germany, as always, will be a candidate for the title, they have to be, but given my personal experience, I prefer to remain cautious.
"We have to show a little more humility, especially when we see what we have produced in the last tournaments."
Flick's side have been drawn in a difficult group for the Qatar tournament alongside fellow European giants Spain, as well as Japan and either Costa Rica or New Zealand.
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