Super League decided to partly split from the governing body in 2017 but, when Davy took over from Robert Elstone in March, he said the plan was to bring them closer together once more.
The need to do so was highlighted last week when Super League planned a full round of fixtures even though England - run by the RFL - had long been set to face the Combined Nations All Stars at the same time.
Both England and the All Stars faced difficulties getting squads together - especially as Covid hit once more - with Hull KR head coach Tony Smith arguing the international should have been postponed.
Davy, the Huddersfield Giants owner, revealed: “It is a reality that the Super League fixtures working group recommended a blank weekend for Super League on the international weekend.
“My preference was for there not to be (games).
“However, the circumstances as such were the (Super League) Board ultimately decided - with pressure on fixtures and so on - there ought to be and I support that.
“Clubs are going through enormous financial difficulties.
“(But) for clarity, the international had no impact on planning (for talks with the RFL).
“The timing was in my plans some time ago.
“The important thing is that the whole game goes forward together. Together we can be stronger.”
A Super League spokesman insisted they are not aware of any clubs saying their players could not be picked by England coach Shaun Wane and Davy maintained the competition had given “tremendous support” to both international coaches.
On talks with the RFL, Davy added: “Discussions and negotiations will be starting probably a week today (Monday), certainly early July,
“It’s impossible to say with certainty but I’m working towards a late August expectation we’ll get to a conclusion.
“I hope we can advance discussions fairly rapidly – I know Simon Johnson and Ralph Rimmer at the RFL are also keen to progress them.
“But realignment doesn’t mean losing the identity of Super League nor does it mean going back to the previous arrangement with the RFL.
“We’re talking about negotiations with the RFL to find a solution that works for the game as a whole. It will almost certainly involve compromise."
Davy also added there had been “formal interest” in showing Super League games on terrestrial television in 2022 as part of the new broadcast deal.