The 24-year-old is the world's leading ODI wicket-taker in the past year with 48 wickets in 19 matches and is Kohli's preferred spin option alongside Yuzvendra Chahal.
"Virat has always had belief in Chahal and me," Kuldeep told cricket website ESPNcricinfo. "He believes both of us can take wickets at any time in a match, that we can change the game at any time.
"He tells us that even if we go for five or 10 runs extra, it's not an issue as long as we're getting wickets. He trusts us, gives us the freedom to bowl the way we want to. He just says, 'I want wickets.'"
Kuldeep and Chahal have taken a combined 77 wickets in the past 12 months, six more than India's pace trio of Jasprit Bumrah, Bhuvneshwar Kumar and Mohammed Shami.
With batsmen at the World Cup already profiting from the flat pitches in England and Wales, Kuldeep says he is working on a strategy to help him cope and would like more overs at the death.
"In ODIs, when you get hit, the plan is to figure out how to force the batsman to rotate the strike so you can bowl at the second batsman to create pressure," he added.
"After 40 overs, the field is a bit more open. It's a bit easier to bowl and the batsmen are taking more chances."
India begin their World Cup campaign against South Africa in Southampton on Wednesday.
(Reporting by Shubham Kalia in Bengaluru; Editing by Simon Jennings)
