Conte's days at Stamford Bridge look to be numbered after a 4-1 defeat to Watford meant that the Blues suffered back-to-back three-goal defeats for the first time in 23 years.
The Italian coach dismissed the notion that he was concerned about his future, but indicated his time may be coming to an end.
"I'm not worried," Conte said. "Tomorrow is another day. I can be the Chelesa coach or not. I try to do everything. If it's not enough, the club can make a different decision. Life goes on.”
A number of successful managers have been tipped to replace the 48-year-old if he is sacked by the Chelsea board, with Luis Enrique leading the race with odds of 2/1 from BetVictor.
Former Blues boss Guus Hiddink is also one of the leading candidates due to his familiarity with the club, with odds of 3/1 on the Dutchman to take charge on a temporary basis until the end of the season. Hiddink has twice worked with Chelsea in an interim role, back in 2009 and then again in 2015-16. In his first stint at the club, he helped them win the FA Cup.
Juventus boss Massimiliano Allegri would be a permanent appointment at Stamford Bridge and is rated 5/1 to leave Serie A for the Premier League. Another Italian is just behind him in the betting order, as Carlo Ancelotti is 6/1 to take charge. Ancelotti is also familiar with Chelsea, having won the Premier League in 2009-10 before being fired the following season.
Atletico Madrid's Diego Simeone (6/1), Celtic boss Brendan Rodgers and Germany's Joachim Low (both 14/1) are also in the running, but one name that is proving popular with Chelsea fans is former Borussia Dortmund manager Thomas Tuchel, who is 10/1 to take charge of the London club.
Like some of the other candidates, Tuchel is currently unemployed, and recently took himself out of the running for the head coaching job at Stuttgart due to his desire to manage a bigger club. Chelsea would fit that profile, with some fans even pushing the #TuchelIn hashtag on Twitter.