Rudiger’s future at Chelsea is under the scanner due to his current contract expiring at the end of the season.
The two sides are in talks over a new deal, but the defender is believed to be demanding becoming one of the highest-paid players in the squad as part of the negotiations.
Bayern Munich are said to be keeping tabs on the player with a view to potentially signing him up on a free transfer next summer.
But Nagelsmann remained coy on whether he is interested in taking the Germany international to Bavaria and stressed that he has not spoken to the club hierarchy about Ruidger.
The Bayern Munich coach said in a press conference when asked about interest in Rudiger: “I am not a fan of talking about players who are under contract with other clubs.
“He is a Germany national team player and has performed well. Thomas Tuchel helped him to get the best out of himself.
“I have never spoken to Brazzo [Bayern Munich sporting director Hasan Salihamidzic] about Rudiger and even if I did, I wouldn’t give it away.
“I don’t even know until when he is under contract and I will check that out now.
“And if there’s some money left in my wallet, let’s see what the future holds.”
Chelsea want to keep him but are believed to be reticent about giving in to his wage demands at the moment.