The Irishman met with Branson on Wednesday at the Pendulum Summit in Dublin's Convention Centre.
The Irish fighting star was present to pick up a lifetime achievement award for his business moves throughout his career.
Somehow the pair then engaged in a face-off, more commonly seen before a huge fight.
As the number two-ranked fighter in the lightweight division, Nurmagomedov appears to have only two fight options ahead of him: interim champion Tony Ferguson, and McGregor, who hasn't defended his belt since winning at UFC 205, where he beat Eddie Alvarez by way of technical knockout.
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Is the world really ready for a sequel to August's boxing extravaganza between Floyd Mayweather and Conor McGregor? Nobody is interested in fighting for a fake belt.
"This is a game of time ... we can't let this thing go on forever and not give other guys the opportunity".
Russia's most popular fighter, undefeated lightweight Khabib Nurmagomedov, who was victorious on the UFC 205 card against Michael Johnson, has always been rumored to headline an event his home country.
"As long as Conor is willing to fight by March, we could do Khabib vs". "And he's going to make a big fight in the future, but I think Khabib and Tony is the big fight and f***, they might even do that one in Russian Federation".