Bielsa said he would quit in November when Jorge Segovia won the ANFP election, but that result was declared null and void because of a clash between Segovia's business affairs and his position as president of first-division Union Espanola.
Jadue, who took office on Friday after winning the second election in little more than two months, said he hoped to make Bielsa change his mind.
"We will make all the necessary efforts to comply with the objective (to retain Bielsa)," Jadue told a news conference.
"People talk about plans, of coaches, but that's totally false. There's no plan B, no plan C," added Jadue about rumours of candidates to follow Bielsa.
Local media said Argentine Jose Pekerman, who followed Bielsa as Argentina's coach in 2004, was the main candidate to take charge of Chile's "La Roja" (the red).
"Bielsa will be in contact with this (ANFP) presidency when he comes back from the U.S. I think we must respect the preparation of the team for this match," added Jadue.
Chile play the U.S. away on January 23.
Bielsa, appointed by former ANFP president Harold Mayne-Nicholls in 2007, signed an extension to his contract after the 2010 World Cup finals in South Africa where they reached the second round.
