The former Hull KR player goes into Saturday evening's clash with Catalan Dragons in Perpignan in the best form of his career and currently tops the Super League scoring chart with six tries in his first four games.
England have a trio of established wingmen in Ryan Hall (Leeds), Tom Briscoe (Hull) and Josh Charnley (Wigan) but the 29-year-old Cockayne said: "It's something that's actually on my mind now because I do feel I'm playing the best rugby I've ever played. I would like to think I'd be in with a shout."
He went on: "You've got Briscoe, Charnley and Ryan Hall so I've a lot to contend with but if Steve McNamara wants something different, I think I can offer him him that."
Cockayne will be hoping to maintain his impressive start to the season when Wakefield take on the Dragons, who have a formidable record at Stade Gilbert Brutus.
"I'm not too sure if I've ever won out in France in my Super League career," he said. "It's going to be a tough challenge but we're in good form."
In Saturday night's other game, Hull will be looking to make amends for an embarrassing 42-16 defeat at Widnes last season when they return to the Halton Stadium.
The Black and Whites have won just one of their first four matches but coach Peter Gentle is confident they are heading in the right direction.
"We're learning about managing games and each week I'm seeing us getting better," Gentle said. "Obviously we want that 80-minute performance but parts of our game are continually improving.
"We all want to win every week but I think everybody has seen some signs that, when this team clicks into gear, we're going to be a formidable side."
- Sports & Recreation
- Josh Charnley
- Tom Briscoe
- Catalan Dragons