It comes after what they described as "a flood of money in the last 48 hours" for Wales flanker Sam Warburton. Warburton's odds went from 3-1 to 4-7 as a result to start the first Test as Lions captain in Brisbane on June 22.
"In the last six months, Warburton has gone from being a rank outsider to the odds-on favourite," Ladbrokes spokeswoman Jessica Bridge said. "Money talks, and it looks like (Lions head coach Warren) Gatland has made up his mind."
Warburton led Wales to the 2011 World Cup semi-finals and a Six Nations title and Grand Slam last season.
But he only captained Wales once during this year's Six Nations, with Ryan Jones leading them three times and prop Gethin Jenkins doing the job in a memorable title-clinching victory over England at the Millennium Stadium.
Warburton was initially injured, missing the win against France in Paris, but then he returned on the bench against Italy, before starting against Scotland and England.
Gatland is not to due to unveil his choice of skipper until the official squad announcement in London on April 30.
Ireland stars Brian O'Driscoll and Paul O'Connell are also among the leading Lions captaincy contenders. Centre O'Driscoll led the Lions to New Zealand in 2005, but he suffered a tour-ending injury early in the first Test.
Lock O'Connell, meanwhile, carried out leadership duties in South Africa four years ago and he has recently enjoyed a spectacular return to form with Munster following a lengthy injury absence.
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