Peskov made the announcement after a bilateral meeting between Putin, a black belt in judo, and British Prime Minister David Cameron. The two met on the sidelines of the G20 summit in Los Cabos in Mexico.
"Putin wished Cameron success in hosting the Olympics and said that he is thinking about visiting London on one of the Olympic days to watch a judo tournament. He will make the decision later," Putin's spokesman Dmitry Peskov said.
Britain's relations with Russia have been sour since the 2006 murder of Alexander Litvinenko, a former Russian spy who died from poisoning by radioactive polonium-210. Many of Putin's foes have also received asylum in Great Britain.
Russia has refused to extradite Andrei Lugovoy, an ex-KGB bodyguard Britain wants to prosecute for Litvinenko's murder.
The incident sent ties between the countries plunging to a post-Cold War low and led to tit-for-tat diplomatic expulsions.
A number of British politicians including former Europe minister Denis MacShane have said Putin should not be welcome at the Olympic games because of human rights abuses in Russia.
Putin last visited Britain in 2003.
Cameron visited Moscow last year, ending a four-year period during which Putin has had no high-level contact with British officials. On Monday, Cameron had to wait for Putin who was late after an extended meeting with U.S. President Barack Obama.
"The Prime Minister kindly agreed to wait and used the pause to work with documents," Peskov said. He said the two leaders exchanged jokes about Euro 2012.
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