Talking to reporters during a promotional programme here, Kumble, however, said that Dhoni was doing well as a Test captain save the eight defeats against England and Australia in the team's last two tours.
"He (Gambhir) has showed his credentials. He has the ability. It's nice to have somebody else in the team who has showed his ability, led from the front and batted well," Kumble said referring to Gambhir's stint with the triumphant Kolkata Knight Riders.
"It augurs well for Indian cricket. But Test captaincy is different from T20. Apart from the eight Tests, Dhoni has done well in the past. I consider this as a leadership group, which is a core group in the team," Kumble said.
Kumble said that it was frustrating to see the once world number 1 team losing eight Tests in a row.
"Defeat can be acceptable when you know that the opposition is dominating, but not when you are a No 1 side. The last time, we were dealt with such a blow was in 2000 Australia series that we had lost 0-3."
However, he hoped that those defeats would serve as a wake-up call ahead of India's upcoming engagements.
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"To see that happen again, was very difficult to digest. Hope this serves as a wake up-call and kick-start a process. Hope they do well in the coming months."
Kumble also spoke about Chris Gayle and his attacking batsmanship.
"He is just amazing. Please don't remind me of bowling to him. In Bangalore before Gayle came in, only three or four sixes were hit out of the park (M Chinnaswamy). But after he came in (to RCB) every season he dispatches at least three out of the stadium.
"The cricket has changed these days with more and more flat wicket. I'm really glad that he is with us at RCB." MORE