The Blues boss is also "coming under increasing boardroom scrutiny" after three games on the bounce without a win, per Neil Ashton in The Sun.
According to Matt Hughes in The Times, many Chelsea stars believe the Italian's continued insistence on "physically demanding [training] sessions, lots of tactical meetings and very few days off" are causing the club's current fitness concerns and affecting Chelsea's form.
Chelsea won the Premier League at a canter last term and were assisted by the fact they had no European football to contend with, meaning Conte often had a full week to prepare for matches.
That has not been the case this season, and already the Stamford Bridge outfit are struggling in their bid to defend the title—they are nine points behind league leaders Manchester City.
The Blues have lost back-to-back matches in the English top flight against City and Palace, and they squandered a 2-0 lead before drawing with Roma.
They have also lost a number of key figures to injury. Alvaro Morata returned from a hamstring problem against Roma, but recent knocks to N'Golo Kante, Victor Moses, David Luiz and Tiemoue Bakayoko could see them all absent for Saturday's clash with in-form Watford.
Chelsea's players "remain supportive" of the manager but are keen for him to alter his methods to prevent fatigue.
However, that does not change the fact Chelsea look understrength and ill-equipped to fight for silverware on four separate fronts in 2017-18.
Their squad is not big enough, and it has been previously reported Conte almost resigned in the summer after not receiving the adequate backing to add to his ranks for the 2017-18 campaign, per Duncan Castles in the Sunday Times.
While money was spent on signing Morata, Bakayoko and Antonio Rudiger, they largely filled the roles of departed trio Diego Costa, Nemanja Matic and John Terry.
Danny Drinkwater, Davide Zappacosta and goalkeeper Willy Caballero were also brought to Stamford Bridge in the summer, but youngsters Nathaniel Chalobah, Nathan Ake and back-up stopper Asmir Begovic were allowed to leave.
The net result is Chelsea's squad is not dissimilar in size or quality to last season.
When domestic football was all they had to focus on, they had the adequate depth to excel. However, that has not so far been true of 2017-18, and Conte's training methods seem to be exacerbating the problem.