The midfielder joined Hull from Tottenham permanently earlier this summer and is hopeful that he can impress Roy Hodgson in his second season at the KC Stadium
The 24-year-old midfielder has one cap to his name, earned while at Tottenham in August 2012, and hopes to add to that tally under Roy Hodgson.
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Asked if being at the KC Stadium permanently might limit his England opportunities, Livermore told Perform: "It shouldn't do, it certainly shouldn't.
"If you look at the World Cup just gone by, I think other countries – not saying this country's got it wrong, but other countries have got it right – [Ron] Vlaar played every minute in every game and was fantastic for Holland and he's at a so-called lesser club [Aston Villa].
"France left [Manchester City midfielder] Samir Nasri behind; these are massive names, massive players, but if they don't fit in the system they want to play they shouldn't be there.
"You have to respect the foreign countries for that approach and that's why they've done so well."
Hull will compete in the Europa League this season after reaching the FA Cup final and that could put some of their star players - including the likes of Livermore, Tom Ince and Curtis Davies - in the frame for potential international honours.
For now, though, Livermore's focus is on continuing the upward trend at the KC Stadium.
"For me it's doing it for myself and doing it for the club who showed faith in me last season," he added.
"If me, Tom or Curtis - whoever it may be - gets a call-up that would be fantastic, but for the time being it's about doing our jobs for Hull City."