The Blues’ hopes of retaining the Premier League title ended weeks ago, and they may not even secure the top-four finish they need to return to the Champions League.
Conte’s side are fifth in the table, four points behind Liverpool, with their next league game at home to third-placed Tottenham on 1 April.
They head to Leicester on Sunday for an FA Cup quarter-final knowing defeat will leave them without a trophy for the second time in three seasons.
Conte, who has been in charge since the summer of 2016, has a contract until the summer of 2019 but has had to deny reports of a rift with the club’s owners.
Speaking last month, the 48-year-old Italian said it is his “intention, will and desire” to stay at Stamford Bridge.
However, Chelsea have lost four of their past six league games, including back-to-back defeats by Bournemouth and Watford.