Julian Nagelsmann met with Chelsea chiefs last week.
The sacked Bayern Munich coach held face-to-face talks with Chelsea football directors Laurence Stewart and Paul Winstanley in Germany. The pair flew out from London last week, says Sky Sports.
Stewart and Chelsea technical director Chris Vivell worked with Nagelsmann at RB Leipzig.
After the dismissal of Graham Potter, Stewart and Winstanley are leading the search for a new manager, but any final decision will have to be ratified by co-owners Todd Boehly and Behdad Eghbali.
Chelsea have also made contact with Bayern about a compensation fee for Nagelsmann, who remains under contract.