The move comes just days after Enzo Maresca was sacked, as the Premier League giants move quickly to appoint a successor, with the former Brighton defender their top target.
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Rosenior, 41, could potentially take charge for Chelsea’s next domestic fixture against Fulham midweek.
After Strasbourg’s draw at Nice on Saturday, he acknowledged there “may be interest” in him but insisted it was “nothing concrete.”
However, L’Equipe report that negotiations with the Blues are far advanced. On Sunday, he traveled to London alongside Strasbourg president Marc Keller and sporting director David Weir to finalize talks ahead of a potential immediate debut.