The deadline for sports to nominate an athlete for the honour has now passed, with a final decision being made by vote among Team GB's senior staff, including chef de mission Mark England and British Olympic Association chief executive Bill Sweeney.
The 36-year-old Wiggins, Britain's most decorated Olympian with seven medals, is understood to have told British Cycling some time ago that he thought it would be better if it nominated a female rider.
The decision will be announced at a reception for Team GB at the BOA's base in Rio, British House, on Wednesday.
Boxer Nicola Adams, tennis star Andy Murray, showjumper Nick Skelton, rower Katherine Grainger and long-distance runner Jo Pavey are among those to have been mentioned with the role.
Sir Chris Hoy led the team into the stadium in London, with speed skater Jon Eley doing the honours at the 2014 Winter Olympics in Sochi.
Of Britain's 45 Olympic flag-bearers since 1906, only six have been women.
There are 206 countries taking part in the Parade of Nations, plus a team of refugee athletes. By tradition, Greece lead the way, with teams then following in alphabetical order, according to their Portuguese names, apart from hosts Brazil, who enter the stadium last.
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