The midfielder joined Bayern from Hoffenheim in January 2017 but has been pushed down the pecking order by the arrival of Leon Goretzka from Schalke.
Earlier this month, Schalke sporting director Christian Heidel rubbished reports Rudy was set to join them.
"I can confirm that Sebastian Rudy has now had his medical examination in Gelsenkirchen," Rummenigge said.
"If he passes it and the supervisory board approves the deal, then it's done. I wish him all the best. He's a great guy, I have to say."
Rummenigge also followed Bayern president Uli Hoeness in confirming the club will not buy a replacement for Kingsley Coman.
The winger is expected to be out for around three months after undergoing surgery on an ankle injury sustained in Bayern's opening Bundesliga win against Hoffenheim on Friday.
"He will be missing for many months. That hurts us," said Rummenigge.
"But we won't do anything in this position. With Arjen Robben, Franck Ribery and Serge Gnabry, we have three good players.
"Serge should be available this weekend again. We trust in these three players and don't plan anything else."