Ancelotti's future at Stamford Bridge has come under scrutiny recently following the shock sacking earlier this month of his assistant Ray Wilkins, after which rumours swirled that Ancelotti had lost faith and was set to leave the club.
The Italian affirmed in midweek that he was fully committed to Chelsea, however doubts were placed on his position again Saturday when Chelsea sporting director Frank Arnesen announced he would leave the club at the end of the season.
The Sunday Telegraph reported that Chelsea want to replace Arnesen with Barcelona's former director of football Txiki Begiristain, and in doing so lure Guardiola to west London.
Guardiola guided Barcelona to the 2009 Champions League title in his first season in charge, and is out of contract with the Spanish league champions at the end of this season.
The report said "sources close to Begiristain" had confirmed that the Spaniard has held talks with representatives of Chelsea owner Roman Abramovich and is "enthusiastic about succeeding Arnesen".