Thompson, who replaced Greg Dyke as director general in 2004, was reported to have told friends that he is “psychologically ready” to leave the public service broadcaster.
Lord Patten, BBC Trust chairman, revealed earlier this week that the organisation had already employed headhunters Egon Zehnder to search for a successor to Thompson.
Candidates for the role could include BBC chief operating officer Caroline Thomson, head of news Helen Boaden and head of BBC Vision George Entwistle.
Other potential applicants outside the BBC suggested by reports include ITV’s director of television Peter Fincham, who previously worked at the broadcaster, and Channel 4 chief executive David Abraham.
The BBC has not made an official announcement about Thompson’s alleged intentions to leave and insists that while it has appointed an executive search firm to find his eventual successor, this does “not signal an immediate vacancy” at the top.
Thompson has previously said 2012 is set to be the biggest year in the BBC’s history, with the broadcaster planning to create a multi-platform social hub to complement its Olympics coverage.
The BBC will also be covering several other big events in the coming months including the Queen’s Diamond Jubilee and the Euro 2012 football tournament.
During his tenure as director general, Thompson has overseen the agreement with the government to freeze the licence fee at its 2010 rate for six years, resulting in an estimated 16% cut in funding to the corporation. Marketing budgets have been slashed by 25% as the BBC looks to bring down costs across the entire organisation.
Read the full interview with Helen Normoyle – her first since being appointed director of marketing and audiences at the BBC – in Marketing Week magazine on 2 February.