Gerrard will leave Anfield at the end of the season after 17 years with the club, 12 of them as captain, and head for the USA to play in MLS.
That will likely take the former England skipper up to the end of his playing career.
Another Anfield favourite, Jamie Carragher, has carved out a reputable career as a television pundit after bowing out from the game in 2013.
But Rodgers believes the "gold dust" that Gerrard could pass on to the stars of tomorrow makes him an ideal coaching candidate.
"I do genuinely believe that he is that type, he can offer great advice," Rodgers told the club's official website. "It's whether it's something that he wants to do.
"When players retire and finish, they have been in this cauldron for so many years and especially with the eyes on you at a club like this here.
"They move away and they might find that after a year or two out of it, it's actually not something they want to do and there are other opportunities for them that are maybe less stressful than moving into coaching and management.
"From my perspective here, the experience that he has of Liverpool as a club and those little bits of gold dust that he can give players would be invaluable to young players."
Though in no doubt over Gerrard's capacity for an off-field role, Rodgers tempered any thoughts that the 34-year-old should move straight into management after playing.
"Moving into coaching and management is not something you just click your fingers and move into," the Northern Irishman added. "There's a lot of work, lot of hours, lot of time and a lot of commitment that has to go into that.
" I always say that if you want to move into coaching or management, take two or three years to really get your eye in on it, because it's not something that you can just click your fingers and walk into - it's a pressure situation.
"You see coaches coming in on the back of managers, learning the ropes and then maybe one day moving on in that field. For Steven, that would be a great opportunity for him to do that, but time will tell if that's something that he's really interested in."
