He is in a similar position to England's Roy Hodgson in that he is planning for Euro 2016 not knowing if he will still be in charge of the national team after the tournament.
The former Juventus midfielder is credited with rebuilding the Turin side in the three years he was manager, from 2011 to 2014, winning three successive Serie A titles.
Abramovich is aware Chelsea's squad needs a major revamp after a dismal attempt to defend their title this season.
Conte's successor, Massimiliano Allegri is also a candidate for the Stamford Bridge job, along with Manchester City's Manuel Pellegrini, who is being replaced by Bayern Munich boss Pep Guardiola at the end of the season.