Rodgers managed the Swans for two seasons before leaving for Liverpool, and Shelvey has revealed that he was contacted by the Scot before signing a deal at the Liberty Stadium.
The 21-year-old told the South Wales Evening Post: "Because Brendan was here, it helped me get to know the club a bit more.
"When I was coming down, he rang me and told me about the club and the people to look out for, the people who would help me.
"It has helped me working with him already, and obviously he can't speak highly enough of Swansea City Football Club. This represents a big opportunity to play a lot."
Shelvey made his competitive debut for his new club during their 4-0 victory over Malmo on Thursday night.