"It is not about individuals but I feel time has come for an Indian coach to take over," Ganguly said at a panel discussion after the launch of inaugural Wisden India Almanack magazine here last night.
Fletcher's two-year tenure ends in March next year and it is widely believed that his contract will not be extended by the Indian Cricket Board (BCCI) given the team's string of poor performances under him.
Under Fletcher, India had lost Test series away and home against England besides also being whitewashed in Australia.
The first copy of the inaugural edition, which features batting great Rahul Dravid on the cover, alongside current India star Virat Kohli, was presented to BCCI President N Srinivasan. The magazine is being published by Fidelis World.
Kohli received a copy of the Wisden India Almanack from Ganguly, currently president of the Wisden India Editorial Board.
"To feature on the cover of the Wisden India Almanack that too alongside a great player like Rahul is an honour," said Kohli.
Also present were current India captain Mahendra Singh Dhoni and Ravichandran Ashwin.