A club spokesman described the reports as "absolute nonsense" and denied that any player had contacted Holland, who left in the close-season to become full-time assistant to England manager Gareth Southgate.
Conte, who played for Juventus under Ancelotti, a Chelsea League and FA Cup winner in 2010, used an expletive in relation to the same reports.
"This is a lack of respect," he told a news conference. "They try to create problems between me, the club and the players.
"It's no good that this person has to send me a message to say this is not true. I hate this type of situation."
Conte faced criticism after successive defeats by Manchester City and bottom club Crystal Palace, followed by a 3-3 draw at home to Roma in the Champions League.
But since then Chelsea achieved a late 4-2 victory over Watford and beaten managerless Everton 2-1 in the League Cup, leading him to deny it was his toughest period since taking over 17 months ago.
"I had a really tough period last season, tougher than now," he said.
The champions, fourth in the table, visit Bournemouth on Saturday looking to repeat a two-goal win there in April.
"Their position in the table is not right," Conte said.
"They played very well in a lot of games but sometimes they were very unlucky."
Midfielder N'Golo Kante could be back for Tuesday's return game against Roma in Italy, the manager added.
(Reporting by Steve Tongue Editing by Jeremy Gaunt)
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