The Everton midfielder rejected a chance to sign with the Blues on deadline day.
But given how a lack of depth has hampered his squad this season, Antonio Conte wants to bring the Englishman to London in January.
Barkley is yet to make an appearance for the Toffees this season as he continues to recover from a hamstring injury.
The 24-year-old is out-of-contract at the end of the season.
Tottenham are also listed as a potential suitor for Barkley.