He will take to the stage alongside the campaign's other highest-profile ambassadors in Zurich, Prince William and former England captain David Beckham.
There is no clear front-runner, and the England bid team will hope that the prime minister's presence will be enough to win over some of the key undecided voters.
With the prospect of such a close contest, it is almost certain that second and third preference votes will end up being decisive.
After each round of voting, if there is no clear winner with more than 50% of the vote, the bid with the least votes will be eliminated.
Cameron's arrival in Zurich two days before the vote will mirror former Prime Minister Tony Blair's decision to travel early to Singapore in 2005, when he was campaigning on behalf of the London 2012 Olympics.
Blair was widely perceived to have stolen a march on his rivals, most notably France president Jacques Chirac, by beginning his face-to-face lobbying before other world leaders arrived in the country.
Russia Prime Minister Vladimir Putin is expected to lead the lobbying campaign for his country's bid in Zurich. It is not yet known when he will arrive in Switzerland.
The Fifa executive committee usually comprises 24 members, with one vote each.
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