Bielsa, who led Chile in South Africa this year where they won their first World Cup matches for 48 years, resigned after Jorge Segovia was elected head of the Chilean federation (ANFP) in November.
However, Segovia was later declared ineligible, leading to speculation that Bielsa - who had previously extended his contract - would stay on. A new election could take place next month.
"Marcelo will prepare the match against the U.S, because it's in his contract," Juan Carlos Berliner, head of the ANFP's national team's department, told Chilean media.
"He will take the appropriate decision once the elections have been held, but until then he will continue to work as usual with the senior national team."
Chile face the U.S. in Los Angeles on January 22.
Spanish-born Segovia won the ANFP's presidential election on November 4 but the board of directors then ruled he had been ineligible because of commercial links between his businesses and his club Union Espanola, of which he was president.
The ANFP's tribunal of honour ratified this decision and called for a new election, which is due to be held in January.
Bielsa is immensely popular in Chile, having taken the team to the World Cup for the first time in 12 years, where they progressed to the last 16 before losing to Brazil.
Their 1-0 win over Honduras in the group stage was their first win at a World Cup finals since 1962, which Chile hosted.
