Downing has mainly been employed as a winger throughout his career but Rodgers believes that the England international could have a place at Anfield as a defender.
The Reds boss revealed that he has discussed the change with Downing and that the 28-year-old is "excited" by the idea.
"I think it is a big possibility that he can play there," Rodgers said. "Time will tell [whether he can do it consistently]. I don't like to just give up on players. I always look at different ways you can play them.
"Stewart has a future as an attacking player but I have had a good chat with him on the role and he is excited about it. That is the biggest thing.
"There is no point putting a player into a position he doesn't want to play. But when you speak to someone and tell them what the future could be, along with the qualities that he has, there is no doubt that in the modern game, he could play that role."
Downing has yet to score a league goal since moving to Liverpool from Aston Villa last summer.