Daniel Vettori.
The Times of India reported Kohli's promotion of Vettori but said it was unclear whether the former New Zealand captain, who quit international cricket in March last year, was under consideration.
India are without a coach, with former captain Rahul Dravid believed to have been approached by the Board of Control for Cricket in India.
Kohli plays for Vettori's Indian Premier League team, the Bangalore Royal Challengers. Vettori has also coached the Brisbane Heat.
