The Germany international's current deal is set to expire at the end of the Bundesliga season, meaning he is currently free to discuss his future with potential suitors.
That has led to claims Bayern have already reached an agreement with the player to join the Bavarians as a free agent in June, although Rummenigge has played down those claims.
He told Sky Sports: "You only have an agreement, when the contract is signed and the player passed the medical tests. We are not that far yet.
"Now the player has to decide, I heard the decision will be made within the next days, so before the end of January.
"And of course it would be very nice, if he decides to join Bayern Munich."