The Irish superstar has asked both the UFC and his management company Paradigm Sports to set up an MMA exhibition match with the kickboxer.
Former UFC champion McGregor, 30, was given an indefinite ban from fighting for his involvement in a a mass brawl which erupted after his defeat to Khabib Nurmagomedov in October.
But he hopes to be back in action this year.
McGregor, who became a dad for the second time last week, tweeted: "I wish to go to Tokyo to face Tenshin Nasukawa in a Mixed Martial Arts exhibition bout.
“Before this summer. Please arrange this, this instant. Yours sincerely the champ champ. @ufc @ParadigmSM"
Nasukawa, 20, was left in tears as the referee called an end to his fight with Mayweather after he was knocked down three times inside the opening round.
But the boxing legend, 41, was laughing all the way to the bank after earning £7million for less than a round's work.
McGregor, who claims he raked in about £78m for his boxing loss to Mayweather in 2017, would expect a similar payday for his part in an exhibition match.
The ex-featherweight and lightweight king was quick to mock the American after his farcical win on New Year's Eve.
He shared on social media: "That 9 milli won’t keep you on top of my list for long, kid #Forbesy."
Nasukawa remains undefeated on his professional record with 26 of his 27 wins coming by KO.
The Far East sensation is also 4-0 in MMA after signing with Japanese promotion Rizin.
McGregor's defeat to Russian champ Khabib was his fourth in the UFC, while he has won his other 21 fights.
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