The club have refused to comment on the status of the 48-year-old, who won the Premier League title in his first season and the FA Cup in May.
But Chelsea player Cesc Fabregas has thanked Conte on social media and wished him “luck for the future”.
Conte took pre-season training this week but ex-Napoli manager Maurizio Sarri expected to take over.
The Blues have reportedly agreed on a compensation package for Sarri, 59.
Should Sarri be appointed, he would be Chelsea’s ninth full-time manager since Roman Abramovich bought the club in 2003.
During three years with Napoli, Sarri has not won a major honour but has guided the club to finishes of second, third and second again – behind Juventus in 2017-18. The former Empoli manager was named Serie A Coach of the Year in 2016-17.
The right decision? Conte quick stats
- Conte’s mark of 30 league wins in the 2016-17 campaign was a record until Manchester City produced 32 in 2017-18
- His league win percentage of 67.1% is better than Sir Alex Ferguson’s 65.2% and only bettered by Pep Guardiola’s 72.8% in the Premier League
- In all he won 69 and drew 20 of his 106 games in charge of the club
- He has won four league titles and a domestic cup in his last five seasons as a club manager
‘Thank you for everything boss’
Chelsea midfielder Cesc Fabregas on Twitter: “Thank you Mister for another Premier League title and FA Cup. It wasn’t easy for me to convince you in the beginning but in the end I hope I did you proud! Good luck for the future.”
Former Chelsea captain John Terry – who left in the summer of 2017 – on Instagram: “Thanks for everything Boss. In a time that should have been the most difficult season of my career, Antonio was honest, respectful and there for me whenever I needed him.
“I loved working and learning from him. Thank you for everything boss.”
Conte pays for stop-start campaign
Conte’s future was under scrutiny even as his side beat Manchester United to lift the FA Cup in May but he remained in place and took pre-season training this week with those players not at the World Cup.
However, his exit has been anticipated all summer after the Blues missed out on Champions League qualification due to a fifth-place finish in the Premier League.
May’s FA Cup final success means Conte – who managed Juventus from 2011 to 2014 – has won a major trophy in each of his last five seasons as a club manager.
In all it proved a fractious campaign for the west-London club, with Conte outspoken about the congested Christmas fixture list and on times visibly agitated in news conferences when questioned about a public war of words with Manchester United manager Jose Mourinho.
Chelsea ultimately finished 30 points behind Premier League champions Manchester City and exited the Champions League at the last-16 stage after a 4-1 aggregate defeat to Barcelona.
In mid-October, the Blues were beaten by a Crystal Palace side who had gone into the match with no points from seven games, prompting Conte to dismiss rumours of unrest over his training schedule.
After Christmas they suffered back-to-back league defeats twice – first by Bournemouth and Watford, and then against Manchester City and Manchester United – and a run of four-straight wins late in the campaign could not secure a top-four finish.
Did missed deals cost Conte?
Two months after guiding Chelsea to the Premier League title with a seven-point cushion in 2016-17, Conte signed an improved two-year contract at Stamford Bridge.
But he was warned not to follow the title success with “a Mourinho season” in reference to their slump of 2015-16 when they finished 10th, a year after winning the league under the Portuguese.
The summer of 2017 saw captain Terry leave Chelsea after 22 years, while Diego Costa was told by text message that he was no longer in Conte’s plans and he eventually completed a protracted move back to Atletico Madrid in January.
The outgoings continued as Chelsea sold Nemanja Matic to rivals Manchester United for £40m.
Although Chelsea strengthened with the arrival of players such as £60m striker Alvaro Morata, they missed out on other targets, including their former striker Romelu Lukaku, who moved to Old Trafford instead.
By January, Conte was answering questions over his future, insisting he was happy and, in early February, he was urging the club to give him a public vote of confidence.
He has reportedly received a compensation payment of around £9m to leave and the club now has less than a month for their new man to make an impact before their Premier League opener away at Huddersfield on 11 August.
Hardest job in football?
Russian billionaire Roman Abramovich took control of Chelsea in June 2003, with Ranieri – the future Leicester manager – already in charge.
Ranieri lasted less than 12 months into Abramovich’s reign, being sacked in May 2004 after almost four years at the club. No manager has lasted that long since.
Chelsea have had eight permanent managers under the Russian’s ownership, in addition to two interim spells for Guus Hiddink and one for Rafa Benitez.
Like a number of his predecessors, Conte has been dismissed the season after winning a major trophy, pointing to silverware being no guarantee of job security at Stamford Bridge.
Chelsea fly in the face of the game’s old logic that stability is the bedrock of success. Owner Roman Abramovich has successfully disproved this theory, as he did when he appointed Conte to replace Mourinho.
The Italian was an inspired choice in that first season, taking Chelsea from 10th to champions and captivating Stamford Bridge with his fiercely driven approach and animated body language that pleased the club’s support, captivating crowds around the Premier League.
Then, as has happened so often at Chelsea, it turned sour quickly. Conte appeared unhappy at the summer transfer activity and was not shy to talk down hopes for this season.
The breakdown in Conte’s relationship with Diego Costa was responsible for the striker’s departure while Nemanja Matic’s sale to Manchester United was more contentious – but Abramovich hardly hid the chequebook and supported him in the market.
Conte has looked to be on borrowed time at Chelsea since last summer but history suggests his departure will hardly shake Stamford Bridge to its foundations. This is a club used to major change and has proved it has the infrastructure to cope.