Foster, who made 244 appearances during a six-year spell with Barnsley before his release last summer, played alongside Stones when the Everton defender made his Reds debut in the Capital One Cup at Rochdale in August 2012.
"He's a lot better player than I was and he can have a lot better career than I did," Foster told the Reds' official website. "I'm sure he will do. He's got all the attributes.
"It was always obvious he had talent, but the most impressive bit was he had a bite about him in his determination.
"His talent was obvious in the games I watched him play in. The reason why he continues to do so well is that he listens. For any aspiring footballer coming through the ranks, that's the most important thing - to listen."
Foster watched Stones make his England debut and added: "It was surreal, everyone associated with Barnsley will have got that sense of pride of knowing him.
"Him doing so well is just great to see. He'll continue to work hard and push on. You always want nice people to do well.
"Every time someone asks me about him, I always say the same thing - two separate managers have described him as a 'Rolls Royce'.
"He's got the lot. He's athletic, he's got the build, he's quick and got good feet."