Nagelsmann could be available after Germany's World Cup campaign concludes this summer.
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Chelsea are seeking a new manager after the dismissal of Liam Rosenior last week and Lehmann told talkSPORT: "Well, if he performs not really well...
"I think he must be exchanged, that's for sure, because we have a different expectation.
"Chelsea were so unfortunate with their appointments of recent coaches.
"Yeah, they can try Nagelsmann."