However, a Parker v Haye fight would be a standalone pay-per-view event and much more lucrative.
"If we went to England and beat up David Haye, Joseph Parker would become an instant superstar up there... and I'm sure the Hearns would be happy for that to happen because it's just going to make the pay-day bigger for everybody when Parker takes on Joshua," Lonergan said.
"For Joseph Parker right now it's probably the highest paying fight in the world for him. So why wouldn't we look at it?
"For David Haye this is the biggest money fight for him in the short term. I know from reading the papers that Tyson Fury ain't keen on fighting David Haye and Anthony Joshua seems to have zero interest because he's not fighting good opponents.
"If he beats Joseph Parker then he is guaranteed a fight against Anthony Joshua."
Haye, who has lost only twice in a 30-fight professional career, has been criticised at home for fighting two vastly over-matched opponents on his return from a three-and-a-half-year layoff. Prior to that he was a cruiserweight and heavyweight world champion; he lost the latter title to Wladimir Klitschko in 2011.
Haye is likely to be in the top five when the IBF rankings are updated which would mean that if he beat Parker he would be the new mandatory challenger for the title held by Joshua.
Lonergan, who described Haye has a "promotional genius", said any future fights hinged on Parker's ability to beat Australian Solomon Haumono in his next bout in Christchurch on July 21.
He felt Carlos Takam, Parker's last opponent whom he beat over 12 tough rounds in Manukau recently, was a better fighter than Haye.