The 18-year-old shone for Monaco as they claimed the French title and reached the semi-finals of the Champions League last season but the forward wants to leave the club "very soon," L'Equipe said in the report.
Monaco recently said it was hopeful that the teenager valued at 180 million euros ($213 million) would agree to a new contract.
With Brazilian striker Neymar on the verge of a record-breaking move from Barcelona to Paris St Germain, according to the player's agent, Mbappe would represent an ideal replacement at the Catalan club should that transfer go ahead.
Monaco did not immediately respond to an email requesting comment.
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(Reporting by Sudip Kar-Gupta; Editing by John O'Brien)
