The 20-year-old, who scored in last night's 4-0 win over Sweden for the England Under-21 side, has insisted that Gerrard is always available to offer the former Charlton Athletic midfielder advice.
"Steven has been first-class with me ever since I came into the club," the Liverpool Echo quotes Shelvey as saying.
"I've moved in next door to him now which is even better because if you need any advice, he is always there. I get to see him quite a bit. I've not popped around for a cup of tea yet but he is always welcome to come around for a game of pool."
Shelvey, who has recently dropped out of manager Brendan Rodgers's regular starting XI, recently signed a new contract at Anfield.