Hatton believes referee Joe Cortez contributed to his only defeat in 44 professional contests in Las Vegas and is keen to face WBC welterweight champion Mayweather again under different circumstances.
If Junior Witter was fighting in my backyard, I'd shut the curtains
Ricky Hatton
"I thought the referee was a little bit harsh, the warnings were only coming one way and I lost my cool a little bit," said the 29-year-old.
"But I don't want to be an old man sat with my pipe and slippers in years to come and be blaming it on the referee.
"So I'd like to have another crack at him with a referee on better form and then if Floyd was to beat me again I could say, 'now you know'."
Before a return fight can be sealed, Hatton must first come through his fight with Lazcano before a possible clash with IBF light-welterweight champion Paul Malignaggi at New York's Madison Square Garden in the autumn.
Malignaggi, a native New Yorker, defends his title for a second time against Lovemore N'dou on the undercard of Hatton-Lazcano.
Mayweather, meanwhile, must negotiate a rematch with Oscar de la Hoya on 20 September, as well as an appearance at WWE's Wrestlemania.
Schaefer added: "While Floyd would have to get past Oscar first, he knows that Ricky has talked about the referee.
"He wants to show that he will repeat what happened the first time and fighting in front of 100,000 fans would be huge motivation for Floyd."
Hatton ruled out a clash with domestic rival and WBC light-welterweight champion Junior Witter, saying: "If Junior Witter was fighting in my backyard, I'd shut the curtains."
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