The Blues started the 2016-17 campaign with four straight wins, but have drawn one and lost two of their last three in England's top flight to drop into eighth position in the table.
It had been claimed that Abramovich was furious following the 3-0 defeat at Arsenal last weekend, but Conte has insisted that he has a good relationship with the Russian businessman.
"I think good communication is important always, with all the people to be very clear on all aspects. It is important this, to be very clear with our players, your staff and the owner," Conte told reporters.
"Mr Abramovich has a great passion for football. To talk with him about football is very interesting, to explain about my idea of football. To have a conversation is very interesting, this situation – I like this. In every situation, if you are very clear it is okay always."
Chelsea will attempt to return to winning ways in the Premier League when they travel to Hull City on Saturday afternoon.