"Duncan has a lot of strength as a coach. He connects well with a lot of players and works quite well with them. But, in some ways, the scope or power that he has to make decisions or to make selections has been a little limited," he said.
"Some of these people (coaches) do have the maturity to be able to understand that when players come to them with a problem, they don't necessarily use that as a way to drop someone. But also the coach sees players from such close quarters, he understands players. So I think he (Fletcher) must have a say (in selection)," Dravid said.
Dravid called for giving more power to Fletcher and making him accountable.
"You want to give people powers and you want to hold them accountable, especially when you have senior, knowledgeable people like Duncan," he said.
"I think his reputation is on the line as well. I think, knowing someone like him, he would want to get more involved and have a say in where his own career and his own reputation is headed," he added.
The former skipper, however, feels that in the last three-four years, the role of coach in team selection has diminished.
"I remember John Wright or Greg Chappell consistently attending selection committee meetings, watching domestic matches. I think over the last three-four years we've seen that coaches have taken a slightly more detached, or slightly more backward, role to our selections. I don't think Gary watched a lot of domestic cricket. Duncan has not really done that as well," said Dravid.
Dravid said Fletcher's knowledge would be of immense help to find a middle-order batsman for India after his and VVS Laxman's retirement.
"He's seen a lot of players ... who's a better middle-order player among Manoj Tiwary, an Ajinkya Rahane or a Shikhar Dhawan or Murali Vijay? At least, to have an opinion, an informed opinion by actually coming and watching some games.''
''The fact that he didn't come and didn't attend the selection committee meeting tells you that maybe that's not in his scope of work, he doesn't have those powers," he said.
India's twin Test whitewash in England and Australia prompted Fletcher to put greater emphasis on fitness and Dravid hoped that it would be reflected in the upcoming England series starting in Ahmedabad on November 15.
"Definitely after the loss, he has put a lot of emphasis on the fitness and certain disciplines of the players and knowing and talking to maybe some of them. Over the last few months, there has been a little bit more focus on fitness and disciplines and the basics in skill levels of some players. Hopefully we'll see some of that in these Test series."
Dravid also praised Fletcher's knowledge and tactical acumen and said the Zimbabwean has a good relation with the players in the team.
"I think, Duncan has a lot to offer in terms of a coach, in terms of the tactics, his knowledge of the game, he works well in that area, he works quite closely with a lot of players... I think the relationship is good within the team."