Paul beat 39-year-old former world champion Julio Cesar Chavez Jr by unanimous decision in his last fight.
The 28-year-old earned a decision victory against 58-year-old Mike Tyson in November.
Davis retained his WBA lightweight title in his last contest after fighting to a draw against Lamont Roach Jr in March.
In January, Davis was ranked number eight in the pound-for-pound rankings.
Paul has been on a mission to try and convince the boxing fraternity of his ability since making his professional debut in 2020.
After beating a YouTuber, a former NBA player and three former UFC fighters, Paul fell to his first defeat at the hands of Tommy Fury in 2023.
But with a disparity of around 65lbs between Paul and Davis in their last fights this bout will do little for either fighter's reputation.
There is also a significant height difference with Paul standing at 6ft 1in compared to the 5ft 5in 'Tank', while Davis will be giving up nine inches in reach.
The contracted weight, number of rounds and size of gloves for the exhibition are yet to be confirmed.
Paul wore bigger 14oz gloves and contested shorter rounds against Tyson, given the former world champion's age.
There are striking similarities to when Paul's older brother, Logan, fought Floyd Mayweather in 2021.
Mayweather, an undefeated five-weight world champion, was 35lbs lighter and six inches shorter than his opponent during that exhibition.
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