Carragher, who has made 723 appearances for the Anfield club, this week announced he will retire from the game this summer.
He has already started his coaching badges with hopes high he will stay in the game.
As a McDonald's ambassador for the 2013 FAW Community Awards, Rush believes there could hardly be a better example for emerging players to aspire to than that of Carragher.
Rush said: "Jamie Carragher was perhaps not as technically gifted as some others, but he showed the will and determination and above all his absolutely incredible loyalty to the club.
"It would be great to see Jamie involved at Liverpool if he decided to go down the coaching route.
"One thing is for sure, whether he stays at Liverpool or not he definitely has the ability to be a top coach."
Rush is convinced the current generation of home-grown stars are being denied opportunities by the influx of foreign talent into the game - but says British players have an advantage they must build on.
Rush added: "A lot of people seem to want to buy up foreign players because technically they may be better, but you have got to have the will to win as well, and that's what we've got more of without doubt."
- Sports & Recreation
- Jamie Carragher