A badly cut Cameron lost to Tua by second-round knockout three years ago.
Cameron's preparation is an interesting one given Barrett and Haye have history - the American lost in five rounds against the "Hayemaker" four years ago.
But when asked about his next opponent's choice of training partner, Barrett said: "That doesn't make a difference.
But when asked about his next opponent's choice of training partner, Barrett said: "That doesn't make a difference.
"Desperate people do desperate things. If he wants to go over there and get beat up by Haye for three weeks, by all means let him. I just hope Haye leaves a little bit for me."
Barrett, 41, is nearing the end of his fighting career. He has fought many from the top-drawer, including Wladimir Klitschko, Hasim Rahman and Nikolay Valuev, as well as Haye, and has a respectable 35 win (KO 20) and nine loss record. By comparison, Cameron, who is 34, has a 28 win (KO 21) and two loss record, but has dipped in and out of the heavyweight division and hasn't fought at the same level.
The Kiwi's last fight was a charity bout against Monty Betham last year, a fighter best known for his rugby league career with the Kiwis and New Zealand Warriors.
Barrett, who has previously announced his retirement only to get in the ring again, admitted it was almost time to hang up the gloves, but preferably after one more fight. Intriguingly, he has left the door open for New Zealander Tua, against whom he has fought twice. Their other bout was in New Jersey in 2010 and controversially ended in a draw, despite Barrett's dominance.
"My hit list is Wladimir Klitschko, Vitali Klitschko, Alexander Povetkin, David Haye or David Tua. If I can get one of those guys for my next fight, I will be happy to ride into the sunset [afterwards]."
Serious talk after a not-so-serious start to his media session. Barrett was only in the ring for two minutes before he was hamming it up for the cameras, raising his gloves and announcing: "This your champion right here. We're taking pictures right now of the champion."