It was learnt that a senior team official made the request to a top official of the local organisers, the Cricket Association of Bengal (CAB).
Earlier Kumble had told the media that the hosts had the squad to adapt to every given condition.
Kumble, who entered the media conference soon after reaching the stadium, exuded confidence that the Eden track would be good.
"I've already said that we have the squad to encounter any challenge and adapt to whatever conditions we get. We are not really worried too much about the pitch. We have all our bases covered," said the bespectacled cricketing legend.
The Indian team held a two-hour net session at the iconic venue in the afternoon. R. Ashwin, the hero of the first Test of the series, was absent from the optional practice session along with Ravindra Jadeja and Mohammad Shami.
Shikhar Dhawan, Rohit Sharma, Virat Kohli, Wriddhiman Saha, Amit Mishra and Ajinkya Rahane all batted at the nets.
Kohli, who had a bad outing in the first Test, was seen going to the pitch of the ball trying to gauge the bounce in the wicket. He batted for quite some time.
Also practicing with the Test squad were One-Day hopefuls chinaman Kuldeep Yadav and pacer Barinder Sran, who joined the team from the National Cricket Academy in Bangalore.
