Johnson, also known as Chad Ochocinco, tweeted to Bush that he'd like to get a "cigar and coffee," to which Bush responded: "@ochocinco email email@example.com. We can stop by MBSH together." MBSH is likely a reference to Miami Beach Senior High School, Johnson's alma mater.
The former Patriots wide receiver's once sterling NFL career has been overshadowed in recent years by allegations of domestic violence. His former wife, reality star Evelyn Lozada, accused him of assault in 2013, an incident which led to a 30-day prison sentence for a probation violation. The judge memorably chastised Johnson for acting too glib during his sentencing. Johnson tweeted last year that the fallout from his arrest "ruined" his career.
The NFL has been reeling from bad press over its past handling of domestic abuse allegations against its players. Last year, NFL Commissioner Roger Goodell instituted a new, stricter policy of punishments if an employee of the league breaks their code of conduct. Johnson's legal troubles, however, came while he was no longer affiliated with any NFL team.
RELATED: Jeb Bush rediscovers the culture war
Ironically, Bush's wife Columba penned an op-ed Monday for the Des-Moines Register calling attention to the plight of domestic violence victims. "The passion, commitment and knowledge of these individuals inspire me to continue working towards raising awareness of this hideous crime that plagues our communities, our states and our country," she wrote. "Meeting individuals working within Iowa’s domestic violence programs reminded me that it is critical for those of us who have a voice to use it with great purpose for others."
Johnson claimed Tuesday that he was "chilling" with Bush, but the Republican's camp told msnbc that while the tweet exchange did take place, no meeting between the two actually did.
However, the overture is reminiscent of another unusual celebrity run-in for the would-be candidate. Earlier this year, Bush was seen palling around with hip-hop star Ludacris, despite the fact that the rapper had once penned lyrics calling his elder brother, former President George W. Bush, “mentally handicapped.”