Conte says that while he admires Vardy, the Blues have never approached the striker during his time at Stamford Bridge.
Chelsea sensing that Conte won't stay at the club for long have already agreed terms with Massimiliano Allegri, who has enjoyed great success at Juventus.
Given the fact that Mourinho is the most successful manager in Chelsea's history and Conte then turned up and won a title in his first season, with largely the same squad Mourinho had heading into a relegation battle in 2015-16, the subplots are numerous.
Barkley, who joined from Everton last week, has not played a single match this season due to a hamstring injury sustained at the start of the campaign.
One manager not under consideration is former boss Carlo Ancelotti.More news: This year's flu vaccine estimated to be less effective: CDC
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The Serie A champions are ready to let the 26-year-old leave the Allianz Stadium as they have identified Bayer Leverkusen's Wendell as his potential replacement.
The United boss infamously labeled Arsenal manager Arsene Wenger "a voyeur" when he was Chelsea manager and has exchanged a series of barbs with former Liverpool, Real Madrid and Inter Milan boss Rafael Benitez - and the Spaniard's wife.
"If in that moment there is a person very close to my auto, I don't know what (might have) happened".
The future of the current Blues' head coach has come under increasing speculation this season, as the relationship between the Italian and the club's board have become strained over Chelsea's transfer policy.
In a media conference on January 9, before his team's League Cup match against Arsenal at Stamford Bridge on January 10, Conte said he would never forget what three-time English Premier League victor Mourinho, had said. "They don't have problem about money", Conte added.
He stepped down at the end of his contract previous year and has expressed an interest in working in the Premier League.
"Now I am fully committed for Chelsea, in this job to work with my players to try also to improve the club in the football aspect", Conte said.