However it is not known whether Guardiola is willing to end his sabbatical from football and Abramovich has made contact with former Liverpool manager Rafael Benítez to gauge his interest in taking charge on a short-term basis.
The club's Russian benefactor made contact with Benitez before Tuesday's defeat in Italy as he assessed his options.
After an impressive start to the season, the Blues have won two of their last eight games.
They sit third in the Premier League table, four points behind leaders Manchester City, who they host at Stamford Bridge on Sunday.
Phil McNultyChief football writer, BBC Sport
Even by Chelsea owner Roman Abramovic's sky-high standards, the sacking of Roberto Di Matteo is ruthless. This is the manager who won the Champions League and FA Cup in May. Chelsea's statement claims results and performances have not been good enough - and yet only a month ago they were top of the Premier League after an outstanding 4-2 win at Spurs. The decision makes it even more abundantly clear that Di Matteo was only keeping the seat warm for the first love of Abramovich's footballing life, former Barcelona coach Pep Guardiola. Will he ever be able to lure him to a club for which managerial instability is a way of life?
Chelsea could become the first Champions League holders to exit at the group stage of the competition.
The club statement continued: "The team's recent performances and results have not been good enough and the owner and the board felt that a change was necessary now to keep the club moving in the right direction as we head into a vitally important part of the season.
"The club faces a difficult task ahead in qualifying for the knockout stages of the UEFA Champions League as well as maintaining a strong challenge for the top of the Premier League while competing in three other cup competitions.
"Our aim is to remain as competitive as possible and challenge strongly on all fronts."
The ex-midfielder won the FA Cup twice and made 175 appearances for the Blues between 1996 and 2002, and took over as boss in the wake of Chelsea's
3-1 defeat to Napoli
in the first leg of their Champions League last-16 tie.
Although Chelsea enjoyed an impressive opening to the campaign, Di Matteo faced
constant questions about Terry,
who was banned for four matches and fined £220,000 by the Football Association for racially abusing QPR defender Anton Ferdinand last October.
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