He has made just two starts league starts since arriving for £15million from Everton in January.
Barkley, 24, wants a return to action so he can win an England place back after the World Cup.
His move to Chelsea has been hampered by a hamstring injury which has limited his impact.
Blues boss Antonio Conte’s future is in doubt and ex-Napoli manager Maurizio Sarri is in the frame to take over.
Reports in Italy suggest his £7m release clause with the Serie A side expires on Thursday — despite them already appointing Carlo Ancelotti.
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