It comes after India's cricket board invited applications for the head coach's role last week, despite the team's excellent results.
But Kohli said the board's invitation for applications was a routine matter.
"There are no problems whatsoever. The team is totally focused on the Champions Trophy," said Kohli.
"There has been a lot of speculation and a lot of things written by people without actually being a part of the changing room, which is very strange."
India face Pakistan at Edgbaston in Group B on Sunday, in what is billed as "one of the biggest matches in sport".
Kohli said differences of opinion were part and parcel of the game.
"In any walk of life there are agreements and disagreements always," he added. "These are normal things. Even at home you do not agree on everything with your family.
"If something is put in place as a process, I don't see why people are creating so many speculations about it."
Captain Virat Kohli has denied reports of a rift with coach Anil Kumble as India prepare to face Pakistan in their Champions Trophy opener on Sunday.