Shelvey completed a £6m switch from Liverpool to the Liberty Stadium last week, with the primary aim of playing consistent first-team football in the Premier League.
The 21-year-old believes that a Three Lions call will come if he finds form quickly under Swans boss Michael Laudrup.
He told The Sun: "If I play every week, I feel I can get in the England squad.
"I'm sure Roy Hodgson's not bothered who you play for. Look at Ryan Shawcross at Stoke. They're not a massive club so I don't think it will affect me coming here.
"It'd be part of Swansea history as they've never had a current England international before. I've been frustrated for three years and it was time to try and make a name for myself."
Swansea have never had an active player named in a senior England squad.