The Italy coach is poised to sign a three-year deal with the Blues after emerging as the favourite to take over from Guus Hiddink, ahead of Diego Simeone, Massimo Allegri and Jorge Sampaoli.
Conte’s impressive CV boasts winning a third consecutive league title for Serie A giants Juventus with a record point tally of 102.
And The Telegraph reports that the One Apple restaurant in Monte Carlo, owned by Conte’s brother Daniele, could host the meeting which facilitates a deal between Abramovich and the 46-year-old.
The Italian has reportedly impressed significantly in previous meetings with Blues’ director Marina Granovskaia.
Abramovich sees Conte as a long term option with the potential to develop the club’s promising young players like Ruben Loftus-Cheek, Kenedy and Bertrand Traore.
Conte has a proven track record in this area, having nurtured a 19-year-old Paul Pogba at Juventus when he signed from Manchester United.
The French maestro made 37 appearances during his first season at the club on the way to becoming one of the most exciting and complete midfielders in world football.
If Conte is appointed, he will likely appoint backroom staff including long-term assistant Angelo Alessio, defensive coach Massimo Carrera, fitness coach Paolo Bertelli, his brother Gianluca, who scouts the opposition, and Mauro Sandreani, who specialises in tactics and talent spotting.
Chelsea will also be hoping Conte can find a place in his team for current coach Steve Holland, who has recently received glowing praise from interim boss Hiddink.
The Dutchman said: “I must thank my team for their courtesy and professionalism, Steve is doing a great job.
“They don’t get the publicity I get every week but without Steve it would have been very different for me.”
Abramovich is also keen to find space for club legend Didier Drogba when the striker’s contract expires with Montreal Impact, while the future of club captain John Terry must also be decided.