Foxes striker Vardy scored 24 top-flight goals throughout the 2015-16 season as Claudio Ranieri's Leicester side won the title for the first time in their history.
The 31-year-old, who could also play a part in England's World Cup campaign, has said that the players within Gareth Southgate's team are "very close" but are prepared to concentrate when playing for the country.
"It is very similar, I am not going to lie," Vardy told The Mirror. "We were exactly the same — very close, always wanting to do things together and having a laugh and a joke at training. But then once we stepped over the white lines, it was a different story.
"It has got the same environment and attitude from all the lads so if we put the work in on the pitch we shall just have to wait and see. I think we do [feel like a club team], particularly with the party atmosphere between us all as well.
"That is how it should be. We have definitely got the momentum going into it with the two results."
England's first game is against Tunisia on Monday.