Goal reports Batshuayi’s agent, Meissa N’Diaye, has arrived in the Principality to hold further talks regarding a move.
Everton had been considering a bid of up £18million ($23m) for Batshuayi, given they are unable to sign him on loan.
However, Chelsea defender Kurt Zouma is already plying his trade at Goodison Park on a temporary basis, with Premier League rules stating a maximum of one player can be loaned to another club at any one time.
Should he complete the move to the Ligue 1 outfit, he would be reunited with Thierry Henry, with the former Arsenal striker and current Monaco manager having previously worked as a coach for the Belgian national team.
Batshuayi would also become the second Chelsea player to move to the Stade Louis II during the January window after Cesc Fabregas.