Fabregas is yet to make a Premier League start this season and has only made one substitute appearance against Watford.
It has been rumoured that Fabregas is not in Conte's plans and it was thought that the Italian had said that Fabregas is free to find a new club.
However, the former Barcelona and Arsenal midfielder took to social media to play down rumours of a rift with the new Chelsea manager.
The Spain international wrote: "Contrary to what has been written, the manager and I have a good relationship and he has NEVER told me that I can leave.
"He said that he counts on me, as I count on him.
"I will continue to fight for this club until the very end and when called upon I will always give my very best.
"I'm fully committed to @ChelseaFC and my only goal is to help them win football matches".
Fabregas also took to social media last season when it was rumoured that he was part of a campaign against former manager Jose Mourinho.