The Spaniard is under pressure after a mixed start to the season for the north London club, as they have now won just one of their last four games in all competitions.
Frustration is building among some supporters, with the Gunners already four points outside the Champions League places in fifth place.
A training ground source told the newspaper that some players “mercilessly take the piss out of” the manager.
Emery has become renowned for saying “good ebening” at the start of his press conferences.
But the report claims that younger players in the squad are openly doing impressions of Emery that go beyond the light-hearted.
The 47-year-old is under pressure to deliver a result when his side face Wolves in the Premier League at the Emirates on Saturday.
Arsenal are unbeaten at home in the league this season, winning three and drawing two.
But the collapse against Palace, which came just six days after a shock defeat away to Sheffield United, means there will be no room for another slip-up.
Emery was named as the successor to Arsene Wenger in the summer of 2018 after the Frenchman ended a 22-year spell in charge of the club.
He won three consecutive Europa League titles while in charge of Sevilla between 2013 and 2016, before lifting the Ligue 1 title, two Coupe de France trophies and two Coupe de la Ligues at PSG.
Emery led Arsenal to a fifth-placed Premier League finish and the Europa League final in his debut season in charge.
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