For years Mundine has been criticised for his choice of opponents and refusal to fight in the United States and Europe against the highest rated champions and contenders.
But in a rare interview on Fox Sports News, a sunglass-clad Mundine said he had offered Cotto $2 million, and Mosley $1.5 million, to travel to Australia and take him on.
“I don’t know why they’re avoiding me, maybe I’m too hot,” Mundine said.
“I even offered to fight them in their own backyards … they don’t even have to pay me. I will pay for my team to fly over, all I ask is for the Australian television [revenue].”
Cotto and Mosley are two of the most high-profile fighters in the middle divisions, although both have suffered losses to superstar Manny Pacquaio that have significantly diminished their market value.
Cotto has a December 3 fight lined up against another Pacquaio victim, Antonio Margarito, defending his WBA Super light middleweight title. Mosley was heavily lambasted for running from Pacquiao during his comprehensive points loss in May and his future remains unclear.
Not to be deterred, Mundine promised to live up to his own hype.