Askren, of course, was comprehensively knocked out by none other than Paul himself earlier this month.
McGregor, who has held both the featherweight and lightweight belts within the UFC, has been involved in a bit of back-and-forth with the YouTuber turned boxer.
This time, 23-year-old Paul shared side-by-side images of Askren and McGregor, with their records both reading 0-1 and the caption: "This is the fight we all wanna see."
He's referring - of course - to McGregor's mega-fight with 50-0 unbeaten boxer Floyd Mayweather in 2017, which McGregor lost via a tenth round TKO stoppage.
However, Mayweather is one of the greatest boxers of all time, and by all accounts McGregor gave a decent account of himself in the ring, especially given the fact it was his first ever boxing bout.
So far in his short career, Paul has faced another YouTube star - AnEsonGib - as well as former basketball player Nate Robinson and Askren.
Granted, he hasn't lost yet, but he also hasn't fought against any actual boxers, either.
Nonetheless, Paul keeps on trying to get Conor to fight him, and even had a jibe at McGregor's earning power while he was at it.
Speaking to his brother Logan - who now bizarrely seems like the level-headed one - on his podcast, Jake said: "In Conor McGregor's third fight in the UFC he got paid $80,000. In Floyd Mayweather's third fight he got paid $7,500.
"And by the way, no one is this room can name who they fought. I will pay you 50 grand if you can."
You can bet that they might have been actually fighters, though.
McGregor has yet to properly set his sights on Paul, perhaps because he has no interest in the fight, but he did refer cryptically to the as-yet-uncodified sport of 'blogger jackass boxing' in a recent tweet.
You don't have to work at Bletchley Park to understand what he means there.
In the meantime, Paul needs to fight someone, and it looks like a more realistic prospect at this stage could be Tommy Fury, brother of heavyweight champ Tyson.
Speaking to ESPN recently, Paul said: "I think it'd be a massive fight.
"He's [Fury's] fought scrubs to make himself look good.
"People will say the same about me, but I've fought guys with winning records like Ben Askren and AnEsonGib. Our teams are talking and trying to figure something out."
We'll have to wait and see how this all pans out.
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