"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 on Time Out, ESPNcricinfo's fortnightly audio podcast.
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.