"Sunny is the best person," 1983 World Cup-winning captain Kapil told Headlines Today television news channel on Wednesday.
"When I played, I used to take his advice a lot of times. I personally feel people like him should come forward and say, 'ok, now, this is the time, we will take responsibility, we can't grow worse than this'," he said.
The Indian board meet later this week to analyse the World Cup debacle.
The team, touted as favourites at home, exited in the first round in the Caribbean two weeks ago after losing to Bangladesh and Sri Lanka in the group phase.
Kapil, who coached India between October 1999 and August 2000, said India should not look for a foreign coach this time.
"If I have a Sunil, I won't call a foreigner," he said of Gavaskar, who worked as batting consultant during the 2004-05 home series against Australia.
"(When I meet him) I will tell him, 'Sunil, please, India needs you, come and take the job," Kapil said.
The Indian board has invited former captains to provide their views on India's poor World Cup performance during the two-day meeting starting on Friday where the subject of the country's next coach is also to be discussed.
India's next international assignment is the tour of Bangladesh in May.