Bayern will face Real at the Santiago Bernabeu for the first-leg of their Champions League quarterfinal tie.
Kane missed the weekend clash with SC Freiburg due to an ankle strain picked up while away with England last week.
However, after the win against Freiburg, Bayern midfielder Joshua Kimmich declared: "I think he'd play even in a wheelchair.
"I suppose he'll be able to play. He'll crawl onto the pitch if he has to. I hope he's fit for Tuesday. If I remember correctly, we've never won there, at least not since I've been here."
However, Bayer management is being more cautious and is barely releasing any information about their star striker's condition.
Bayern coach Vincent Kompany said before the Freiburg match that he expected him to be available against Real Madrid, although yesterday he was still being treated by the physios.
This season, Kane has hit a staggering 40 goals in 48 games for the German giants.