A victory for either Martin or Joshua will ease the door open wider for a mandatory shot by Parker, who is ranked No6 by the IBF, an organisation which has no official No1 or No2-rated fighters.
After champion Martin, the next on the list is No3 Erkan Teper, a Turk who failed a drugs test in December and, should his B sample also test positive, is facing a lengthy ban. Fourth is Joshua, with 35-year-old Cameroonian-Frenchman Carlos Takam fifth, one ahead of Parker.
Should Teper drop out due to a drugs ban, Parker could be fighting Takam in an elimination bout for a mandatory shot at the title.
Parker's next fight is in Christchurch on April 16 against an opponent Lonergan hoped he would be able to confirm in the next few days.
Parker is also slated to fight in July, a bout which his promoters hope will be a warm-up for much bigger things to come.
"Right now, what's happening in England is incredibly significant for us," Lonergan said. "With Martin signing to fight Anthony Joshua all sorts of interesting things open up. That's a brilliant fight to be made for British boxing. Britain is a hotbed of heavyweight boxing and it just got a lot hotter."
Joshua, a 25-year-old Olympic gold medallist is an extremely powerful puncher and will present the relatively inexperienced Martin with easily the toughest challenge of his career. Joshua, unbeaten in 16 professional fights, will also be on home turf at the O2 Arena, a fight almost guaranteed to be a sellout.
The Englishman recently said he had been following Parker's career with interest and believed the two would meet in the ring eventually.
IBF standings:
Champion: Charles Martin
1. Not rated
2. Not rated
3. Erkan Teper
4. Anthony Joshua
5. Carlos Takam
6. Joseph Parker
7. Vyacheslav Glazkov
8. Steve Cunningham
9. Andy Ruiz
10. Bermane Stiverne