Putin's spokesman Dmitry Peskov followed up by saying that the president is considering travelling to the event to watch the judo competitions. A judo black belt himself, Putin's choice of event comes as no surprise.
Putin has used judo as a tool of diplomacy before. On a 2003 state visit to Japan -- with the two countries' dispute over the Kuril Islands a constant background rumble -- Putin kitted up and threw some moves at the Kodokan judo headquarters in Japan.
The Russian president has always used his judo prowess to boost his macho profile, along with deep-diving in Lake Baikal, fishing bare-chested, and shooting a tiger with a tranquilizer gun.
In Pictures: Vladimir Putin's Lessons In Machismo
In 2009, after a spot of sparring with some Russians judokas, he offered to join the national team. And the year before that, he released a DVD, "Let's Learn Judo With Vladimir Putin."
Judo has always been more than a sport for Putin. As he told NPR in 2001: "I think it's also a philosophy in a way, and I think it's a philosophy that teaches one to treat one's partner with respect. And I engage in this sport with pleasure and try to have regular practices still."
There is, of course, another side to Putin's love of the martial art -- and it's less about promoting mutual respect and fostering friendship and more about the tough kid growing up on the streets of Leningrad.
Writing in "The Guardian" when reviewing Masha Gessen's biography of Putin, James Meek wrote:
It might not be too much of a stretch to suggest that Putin has applied the lessons of judo -- the nimble sidestepping, the stealthy art of using the weight of your opponent against him, the combination of patience and ruthlessness -- to his political career. This is something that, in the wake of mass opposition demonstrations in Russia this year, Georgy Bovt pointed out in "The Moscow Times":
Putin purposefully let the opposition expend all of its energy on the streets. Then, as many had expected, the opposition stumbled over the following six months as members proved unable to agree on any unified action, leadership, a political program or tactics for pursuing their goals.
Putin is especially known for his Harai Goshi, a move that combines a hip throw and a leg sweep. The move originated as a way to prevent your opponent's sidestepping escape, before pounding them down onto the floor.
What Putin might be trying to do with a possible London Olympics visit could be more about preventing his opponent from escaping rather than about throwing him down.
Putin has not visited the United Kingdom since 2003 and relations between the two have been strained in recent years, particularly since the 2006 killing of former KGB officer Aleksandr Litvinenko in London, which British authorities believe was carried out by the Russian secret service.
In the light of certain European leaders not attending the Euro 2012 soccer championship in Ukraine because of the jailing of former Prime Minister Yulia Tymoshenko, perhaps Putin is thinking ahead to the Sochi 2014 Winter Olympics and the potential embarrassment of high-level nonattendance.
Presidential spokesman Peskov told journalists that Putin wished Cameron every success in hosting the Games. That might well be the tactic: show willing now, rebuild ties on a superficial level ahead of 2014, and the likes of Cameron will return the favor. Or he might just be there for the love of judo.
WATCH: Putin practices his judo
-- Luke Allnutt