"We'll see what the chances are for Roman to come back," Bianchi said at his official unveiling on Wednesday.
Riquelme, 34, left Boca after they lost the South American Libertadores Cup final to Corinthians, citing exhaustion.
According to media reports, he did not get on with former coach Julio Cesar Falcioni and had grown tired of his unadventurous tactics.
Bianchi, Boca's most successful coach in his two previous spells, was officially unveiled on Wednesday as Falcioni's replacement at the club's Casa Amarilla training complex where he signed a three-year contract.
"The decision is Roman's, everyone is the owner of their own decisions. I'll speak with him and see if he is prepared (to return)," said Bianchi, who quit as Boca coach for the second time in 2004.
"I know what Roman can give the team, but until I meet with him I can't say anything else," he added.
Club president Daniel Angelici told Infobae: "If there's anyone who can make Riquelme change his mind, that person (is Bianchi), that's a chance Carlos can go for, speaking to him face to face."
Riquelme did not retire from football and has been courted by Brazilian clubs including Cruzeiro and relegated Palmeiras, after saying he would not turn out for another Argentine side.
Former Argentina coach Sergio Batista tried to persuade Riquelme to join his Chinese team Shanghai Shenhua.
Bianchi, nicknamed Viceroy when he coached Velez Sarsfield where he began his playing career, won four Argentine leagues, three Libertadores Cups and two Intercontinental Cups during his two previous spells at Boca between 1998 and 2004.
Riquelme shared in all but three of those trophy wins. (Reporting by Luis Ampuero; writing by Rex Gowar in London; editing by Toby Davis)