Hall of Fame retired referee Joe Cortez would love to see UFC superstar Conor McGregor and two division champion Paul Malignaggi settle their differences in the boxing ring.

McGregor and Malignaggi have been trading verbal shots for several months.

McGregor, a two division champion in the UFC, made his professional boxing debut in August, and he was stopped in ten rounds by five division world champion Floyd Mayweather Jr. at the T-Mobile Arena in Las Vegas.

Malignaggi, who retired from boxing earlier this year, was hired as a sparring partner by McGregor, to help the UFC fighter prepare for the scheduled battle with Mayweather.

Malignaggi quit after members of McGregor's team released images of their second sparring session on social media.

The images painted what Malignaggi claimed was a "dishonest" picture of the sparring session - as one image showed Malignaggi down on the mat from a claimed knockdown and other images showed him taking punishment.

Then UFC President Dana White released hand-picked video clips from the sparring session. One clip showed a debatable knockdown of Malignaggi and the other had McGregor doing damage.

Cortez was also a member of the McGregor's camp. In fact, he was the referee for the sparring sessions between McGregor and Malignaggi.

Based on what he witnessed in the sparring sessions, Cortez told Helen Yee Sports that a McGregor-Malignaggi boxing match would be a very good fight - and even better than McGregor's contest with Mayweather.

"I would really push for that fight to happen because I feel that a lot of fans would like to see what really happened in that sparring session," Cortez said. "It got a lot of interest. Because people wanted to know what was going on with Paulie and McGregor in that sparring session.

"I can tell you that I was there for twelve rounds with them and there was a lot going on. A lot of boxing fans and MMA fans want to know and I can tell you from being there that the fight should happen. It was very competitive. That is what I am saying. I know for a fact that it would make a good fight. It would be a better fight than McGregor vs. Mayweather.”

“I got to speak with Paulie after that [Mayweather fight]. I told him that to shut everybody up maybe he should have a real fight (with Conor), now that McGregor showed that he actually has some talent. They should put Malignaggi and McGregor together. I think that would be a great fight and that the fans would buy that. Because it would be interesting.”