Barkley agreed personal terms with the Stamford Bridge club after Everton had agreed a £35m transfer fee, but then changed his mind and returned to Merseyside from London.
Barton told talkSPORT: “I heard a really interesting thing about what happened with the Ross Barkley transfer. Conte turned his phone off and Barkley’s representatives were trying to contact him.
“He wanted to say ‘look, where am I going to play’, and Conte turned his phone off. That is why Barkley got cold feet and never signed.
“He thought, ‘well, if the manager isn’t answering the phone to me he clearly doesn’t want me’, and that is why he went back to Everton.”
Barkley is currently recovering from a hamstring injury and is not expected to be available until the end of the year.