Kohli had earlier suggested the Royal Challengers Bangalore coach's name for coveted post to the BCCI.
"I don't see it as a controversy at all. All these things do come up in a scenario when you have to appoint someone (coach). I don't know how it has come out now. I spoke to him a while back. We have spoken to a few other people as well and everyone knows about it," Kohli was quoted as saying by The Times of India.
However, the Board of Cricket for Control in India (BCCI) is still searching for Ravi Shastri's replacement and is yet to finalise over it after ICC World T20 2016.
Vettori, the 37-year-old former left-arm spinner, retired from international cricket following his side's loss to Australia in the final of the World Cup 2015 in Melbourne.
Vettori has taken 362 wickets in 113 Tests and 305 wickets in 295 ODIs during his illustrious career spanning 18 years. Vettori, who has been coaching RCB for the past 2 years, is also the coach of Big Bash team Brisbane Heat.