Rahane didn't have a great series against England and was eventually ruled out with a fractured hand, while he managed just 13 and 18 in the opening Test against Australia in Pune, which India lost by 333 runs.
In total, he has scored 204 runs in his last five matches.
“There is no question of dropping Rahane. He has scored really well, he has been extremely successful over the last couple of years. In terms of team composition we still haven't discussed on that. All 16 are available," Kumble told reporters ahead of the second Test, starting on Saturday.
Kumble though felt it was unfortunate that Nair had been warming the benches.
"Yes, it's unfortunate that Karun missed out after scoring the triple hundred. But that's the way the composition of the team has been. We have always looked to play five bowlers and it's unfortunate that he came in as a replacement. It is nice to have these kinds of choices in the team," said Kumble.
"People have been successful in a group. That's the beauty of this group that whoever came in has done really well but there have been times when people were left out because of team composition and combination. But Karun is a class act and we have seen his short international chances he has got."
On whether the team would go with five bowlers in the upcoming Test, Kumble said they would go with the "right combination".
"It all depends on what we believe is the right combination to win a Test match. If we believe that four bowlers are enough or five bowlers are needed, which four or five bowlers all that depends on what we look at. Our aim is to win a game."
Talking about Chinnaswamy wicket, Kumble said he was expecting it to be a result-oriented track.
"I don't know much about the Chinnaswamy wicket, to be frank. I have grown up playing on this ground but it is generally been a good batting surface. I'm sure it will be a result wicket and that's exactly what we want in a Test match.
Kumble said pitch conditions never bothered him during his playing days.
"In my playing days, I never looked at the pitch. People wrote a lot about my bowling with regard to pitch but as a bowler or captain or coach, I never bothered to look at the pitch. Yes, we go there look at the pitch and come up with what you need to do and decide what kind of strategies you need to put with regard to what you read looking at the pitch," he said.
India lost to Australia in the first Test of the four-match series, ending their 19-match unbeaten streak, and Kumble felt that the players failed to adapt to the situation.
"I don't want to look back, we are here to look ahead. As a coach, it's more important for me to look ahead. It was one of those games where things didn't go our way but you just need to move on. There are another three Test matches in the series. What has happened has happened, it is done and dusted. You can't really worry too much about that," said the coach.
"Australia played well, we didn't play really well. The surface was challenging but we didn't adapt. Every game you need to adapt to whatever comes in your way and that's exactly what we are looking forward to.
"We had a fantastic home season. You can't keep winning every game. Like I mentioned winning games in the current scenario of Test cricket is quite challenging for an international side. That's what this team has been able to do, across conditions be it Sri Lanka, India, West Indies and against quality sides, we have won from difficult situations. We have adapted to various conditions and situations and that's what we didn't do in the last game and that's why the result didn't go our way. We are now looking forward to this game to again start on the winning note," he explained.
Asked about India not using DRS properly, Kumble said, "We keep talking about it (DRS) but I don't think we messed it up. If you look at the two series, we certainly did better than the opposition, both against England and Bangladesh. It's too early to talk about that. You can always have hindsight and expect that you could have missed out but those calls were pretty close. I don't see a reason why we need to worry too much about that."
"Australia are a quality side. I don't think we played to our potential and that's what we will like to do. We will like to comeback into this Test match and play to our potential. We only look at what we need to tick. If we keep ticking on these boxes, results will go our way and that's what we will like to do here. We didn't tick those boxes in the last game and so we didn't win," insisted Kumble.
He revealed that the players took a day off in Pune to go for trekking.
"It is important to keep your mind fresh when things don't go your way or as per planned. So in Pune, we did a different kind of thing. We went out and did trekking and were away from cricket. It is important to unwind because we were constantly playing for the last 10 months. Sometimes results will be in your favour, sometimes not. So it is important to maintain team bonding and keep the players' spirits high. If you don't practice for one day your ability doesn't go down. What mind thinks is important," he adds further.
(With inputs from PTI)