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Conte’s side produced a limp display and could easily have lost to a Leicester team who missed a host of first-half chances.
Even when Leicester left-back Ben Chilwell was sent off midway through the second half for two bookings, the champions were unable to snatch a winner.
Chelsea remain third — 15 points behind Premier League leaders Manchester City — and have drawn their last four matches in all competitions.
The result capped a difficult week for Chelsea boss Conte, who could be in the final months of his turbulent reign despite last season’s title triumph.
Responding to a report claiming he will leave at the end of the season, Conte this week said “everything is possible” regarding his future.
Conte has been linked with a move to Paris Saint-Germain as his relationship with the Chelsea board has grown increasingly fractious following disagreements over transfers and the Italian’s feud with Diego Costa, which led to the striker joining Atletico Madrid.
Conte has reportedly frustrated some of his players with his intense personality and demanding training sessions and their inconsistent performances this season have added fuel to that fire.
Chelsea are reported to be considering Juventus boss Massimiliano Allegri and former Barcelona coach Luis Enrique as potential replacements for the 48-year-old.
“I think a lot of our players were tired. In the first half Leicester ran more than us,” Conte said.
“We suffered a lot. We are not conceding, but we are not creating chances.”
Given the speculation surrounding their manager, it was intriguing to note the response of Chelsea fans.
Having grown used to big-name managers coming and going in the era of owner Roman Abramovich, they hardly seemed heartbroken at the possibility of another change on the bench.
When a chant of Conte’s name emanated from the stands soon after kick-off, it quickly petered out and the Italian responded with only a bashful clap towards the supporters.
Shinji Okazaki had a chance to further dampen the muted atmosphere in the eighth minute when the Leicester striker slid in to meet Chilwell’s cross, but couldn’t control a close-range shot that ballooned over the bar.
– Lethargic Chelsea –
When Jamie Vardy fired narrowly wide from a tight angle moments later, Conte wore a thunderous expression on the touchline.
It took a superb save from Thibaut Courtois to prevent Leicester taking the lead their pressure deserved as the Belgian plunged to his right to claw away a Wilfred Ndidi header.
Chelsea threatened when Eden Hazard teed up Cesc Fabregas for a powerful drive that Kasper Schmeichel palmed away.
But misplaced passes and lapses of concentration littered Chelsea’s play.
Vardy was a constant menace and Conte’s defence again failed to corral the England international, who found space to shoot just wide.
An injury that forced Chelsea captain Gary Cahill off late in the first half added to Conte’s problems.
Fabregas nearly put Chelsea ahead against the run of play, but the midfielder’s drive was tipped over by Schmeichel.
A key cause of Chelsea’s erratic form has been Alvaro Morata’s struggles and the lacklustre Spain striker has now gone five games without a goal.
Chelsea were still in disarray after the interval and Riyad Mahrez’s deflected effort almost crept in, prompting Conte to send on Willian and Pedro for Hazard and Fabregas.
The decision to remove Hazard drew jeers from the frustrated Chelsea faithful.
Conte’s men were gifted an unexpected lift when Chilwell, booked moments earlier, lunged into a studs-up tackle on Victor Moses in the 68th minute, earning a red card from referee Michael Jones.
However, the best Chelsea could manage were harmless long-range strikes from N’Golo Kante and Marcos Alonso as Leicester held firm to leave Conte grumbling his way down the tunnel at full-time.
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