It shapes as a huge test for Mauricio Pochettino's men, who have struggled to find form and fluency this term, winning three of nine matches in all competitions.
Star striker Kane conceded the speculation that surrounded several squad members during the close season has been a challenge and Rummenigge thinks the England captain's own future could provide headaches for manager Pochettino.
"They have a good team," Rummenigge told reporters as Bayern prepared to fly to London on Monday.
"The question is whether they can keep this top team together for a long time, because Christian Eriksen's contract expires next year.
"There are certainly also clubs that are interested in Harry Kane."
He added: "Kane is a top player who, like Robert Lewandowski, scores an incredible number of goals.
"They are perhaps the two best strikers in the world right now.
"I hope Robert will do better than Kane tomorrow but it's not easy to stop him, he's a world-class striker."
Tottenham were not alone in having to manage uncertainty during the previous transfer window, with Bayern involved in one of the most-prominent sagas.
The Bavarian outfit aggressively pursued Leroy Sane until the Manchester City star suffered a serious knee injury in August.
Bayern president Uli Hoeness has since revealed the winger's fitness will be assessed in January ahead of another possible approach, but Rummenigge is paying little thought to the situation.
"To be honest I have no eye on him at all because I don't speak about players that are still under contract at other clubs," he said.
"FIFA rules don't allow that and I will always stick to that."