The brothers, various domestic media suggested, were due to join the Top 14 side after the conclusion of the 2015 Rugby World Cup in November on a two-year deal.
But Altrad said: "I categorically deny these reports."
He added: "And what troubles me a lot is that all this could hurt the players..."
The Du Plessis brothers were crowned world champions with the Springboks in 2007 under then manager Jake White, who joined Montpellier at the end of last year as consultant.
Hooker Bismark, 30, and his two-year older sibling Jannie are expected to form part of the Springboks' front row at the World Cup.