Rummenigge indicated that Gotze will see little playing time if he decides to see out his contract.
He said: "Mario has to consider for himself whether he wants to constantly get minutes."
On Monday, Gotze had also switched agents and is now represented by his family as well as Munich-based agent Prof. Dr. Peter Duvinage.
According to kicker, the switch of agents also saw Gotze's imminent transfer to Liverpool collapse. The report said a €25 million move had been agreed by his former representatives Sports Total, and would have bumped up his wages to €12m a year.
Germany boss Joachim Low and team manager Oliver Bierhoff this week welcomed Gotze's decision, with the latter saying it will allow the player to focus on Euro 2016, and Rummenigge said that may be the reason for the announcement.
"I talked to him, also Ancelotti. Mario knows Bayern's thoughts," he said. "Maybe he just wants to go into the European Championships without any speculation."
Stephan Uersfeld is a Germany correspondent for ESPN FC and runs a blog Dietfried Dembowski. Follow him on Twitter @uersfeld.