It is understood that Wiggins, 36, told British Cycling in July that the honour should go to a female rider.
With seven medals, including four golds, he is Britain's most decorated Olympian alongside fellow cyclist Sir Chris Hoy, who was flag bearer in 2012.
Boxer Nicola Adams, long-distance runner Jo Pavey and tennis player Andy Murray are among the contenders.
The decision will be announced by the British Olympic Association on Wednesday.
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Sir Bradley Wiggins has ruled himself out of being Team GB's flag bearer at the Rio Olympic Games opening ceremony.