McGregor and Malignaggi have endured a bitter rivalry stemming back to their time spent training together last summer.
Malignaggi was brought into Team McGregor to help the Irishman in preparation for his money-grab boxing cameo against Floyd Mayweather.
Things soon became bitter between the two as photos of the sparring sessions leaked – which prompted Malignaggi to depart from McGregor’s Las Vegas training base.
After the American left the camp, a sparring video between the two fighters was leaked including footage of a disputed knockdown of Malligangi.
Since the leaked photos and footage Malignaggi has constantly called McGregor out for a showdown in the boxing ring.
Promoter Hearn told IFL TV he would love to put the fight together, with sports streaming service DAZN the broadcasters.
Hearn said: “I said to (Malignaggi) this morning, I’d love to do it. DAZN, Oh they’d pay a lot of money for that fight.
"I said it to Conor McGregor’s guys I’m going to float them the numbers to them see what they think.
"As I said to Conor McGregor’s guys, maybe he can beat Paulie Malignaggi, I don’t know."
Hearn turned to Malignaggi and said: “It is a good fight. Didn’t he drop you in sparring?
"As far as I’m concerned he knocked you out in sparring. We need to make this as big as possible.”
McGregor has not fought in the boxing ring since he made his professional debut against Mayweather in August 2017.
Mayweather ultimately halted McGregor in round ten of a fight that generated an estimated $550 million with 4.4million pay-per-views sold.
Since that defeat McGregor returned to the octagon to face another rival, Khabib Nurmagomedov, at UFC 229 for the lightweight title.
McGregor was submitted in the fourth round of the fight leaving his future and next opponent up in the air.
The Irishman’s trainer, John Kavanagh, spoke on Joe Rogan’s podcast after the UFC 229 loss and claimed a move back into the boxing world was a possibility.
Kavanagh said: “There are all sorts of crazy rumors going around the management team and the fight team about what might happen next.
"It could be boxing, it could be (Malignaggi), it could be Floyd. All sorts of names are being thrown about.”
Kavanagh added a Netflix documentary on McGregor's training camp in the build-up to the Mayweather fight is set to be released.
Footage of the infamous sparring sessions between McGregor and Malignaggi is set to feature.
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