The 48-year-old led the Blues to Premier League glory last year but his relationship with the board remains strained after a succession of public rants over the club's transfer strategy.
However, some key figures at Chelsea feel that Conte is merely covering for his own shortcomings this season in an attempt to ensure that his hopes of landing another top job are not damaged by his side's dismal title defence.
His departure has looked inevitable since last summer. Although Conte renewed his contract with the club, securing himself a pay rise in the process, he did not extend the length of the existing deal beyond 2019.
Conte has repeatedly denied that he will leave at the end of the current campaign and insisted after Wednesday night's 3-0 loss in Barcelona that he intends to see out his contract, which remains a possibility.
However, contingency plans have already been put in place regarding a replacement, underlining that Chelsea believe that a parting of the ways is almost inevitable.
Former Barca boss Luis Enrique remains the front-runner, while Chelsea are also chasing a director of football and contact has already been made with Juliano Belletti, who spent three seasons in west London during his playing days.
Chelsea will face competition from Paris Saint-Germain for Luis Enrique, though, as the treble winner is also being considered as a replacement for Unai Emery, who is almost certain to leave the Parc des Princes this summer in the wake of the club's tame Champions League last-16 loss to Real Madrid.
Conte is also on PSG's shortlist, while the Italian Football Federation (FIGC) have also revealed that the former Juventus boss could be asked to undertake a second stint as the coach of the national team.
However, the former Azzurri midfielder is keen to continue in club management and contrary to reports that he wants to return to Italy, he has no major preference in terms of which country he manages in next.
Still, given he has clashed with his employers over transfers at both Juve and Chelsea, he is expected to seek out an ambitious club that will back him completely in the market, making the PSG job particularly appealing.
What is clear, though, is that he is unlikely to stay at Stamford Bridge beyond the summer. Indeed, Conte was asked at the end of Chelsea's second-leg loss at Camp Nou whether he will be leading out Chelsea next season and he told Mediaset Premium, “That’s a very naughty question and I prefer not to answer!”
The decision whether to stay or go could yet be taken out of his hands, though. If Chelsea fail to force their way back into the Premier League's top four between now and the end of the season, the Blues board would be inclined to push Conte towards the exit door – if he is not already walking towards it.