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The England coach is out of contract after steering his side to the World Cup final.
But despite the backing of his players and the RFL, he is refusing to reveal his plans.
England second rower Whitehead said: “Hopefully Wayne will stay on but we don’t know when he will decide.
“We can compete with the best and we proved that.
“The Aussies were on their last legs in that last 10 minutes and just waiting for that final whistle.
“They all came up and congratulated us on a great World Cup. We are building something special here and building a great team.”
Bennett has hinted he may coach New Zealand again, but with England not in action again until next summer the RFL are in no rush to demand a decision.
The 2017 Rugby League World Cup host stadiums

But with or without Bennett, Whitehead insists England will soon rule supreme despite Saturday’s agonising defeat.
World champions Australia retained their title but only after the fright of their lives.
“They have got superstars in Cam Smith and Billy Slater but they are going to have to move on soon so it is really going to open up for us.
“We can keep rebuilding and hopefully claim that top spot soon. We have got our own superstars and we are really building something.
“A lot of these players will be around next year as well and hopefully we can build on what we have already built.”
Only Boyd Cordner’s 15th minute try, after Kev Brown missed a tackle, split the two sides in the end.
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Michael Morgan had a second half effort disallowed for obstruction, while Josh Dugan saved the game for the Roos with the tackle of his life.
He ankle-tapped Kallum Watkins to deny England a certain try and Australia hung on in a gripping final.
Whitehead added: “We had the belief we could come here and win and it’s disappointing that we didn’t finish off some of the opportunities.
“But we cannot look back on it - we have got to look forward and keep building on what we’re building.
“We have proved we can defend, we have just got to get better at finishing our opportunities and we are not far off that.”
Full back Gareth Widdop added: “It’s hard to take. It was a huge opportunity and huge effort. We put everything out there.”