He has refused to comment to AFP on reports that he will take charge of the Paris outfit for the 2018/2019 season and sign a three-year contract as successor to New Zealander Greg Cooper.
Former All Blacks full-back Cooper quit Stade two months ago to be with his ill daughter in New Zealand.
Stade lie 12th in the French Top 14 table with five rounds remaining having won just seven of 21 matches, and are just two points above relegation-threatened Oyonnax.
Their squad includes four former Springboks, fly-half Morne Steyn, props Heinke van der Merwe and Gurthro Steenkamp and loose forward Willem Alberts.
Meyer, 50, has not coached since resigning after taking South Africa to third place at the 2015 Rugby World Cup in England.
He was in charge for 48 Tests, winning 32, losing 14 including a stunning World Cup defeat by Japan, and drawing two.
Earlier, he transformed the Pretoria-based Northern Bulls into the dominant southern hemisphere franchise force, winning the Super Rugby title three times in four seasons.
He also coached English Premiership club Leicester Tigers for one season.
Meyer had been expected to sign a four-year extension to his contract as Springboks coach after the World Cup, but pulled out following talks with officials.
A sticking point might have been the racial transformation of the team with Meyer facing constant public and media criticism for choosing predominantly white sides.
SA Rugby and the government have agreed that half the Springboks team at the 2019 World Cup in Japan must be black.
Whites comprise less than 10 percent of the South African population and the government has constantly complained that the Springboks do not reflect the racial make-up of the country.
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