The Argentine has turned down the chance to return to international management, indicating that he is now ready to finalize his "tentative agreement" with Olympique de Marseille.
La Albirroja have been looking for a new permanent boss following sacking of Gerardo Pelusso last year, with Victor Genes having been placed in temporary charge for the final stages of a dismal 2014 World Cup qualification campaign.
Dominguez had hoped to land Bielsa, who has been out of work since parting company with Athletic Bilbao last summer, but the former Argentina and Chile boss has turned down the opportunity to return to the international arena.
"Yesterday morning Bielsa called me to communicate that he was dismissing the possibility of leading the Paraguayan national team," Dominguez told Radio Monumental.
Bielsa, who has been repeatedly linked with Barcelona in the past, is believed to have turned down the job because he is now ready to finalise his "tentative agreement" with Ligue 1 outfit Olympique de Marseille.