New ANFP president Sergio Jadue hopes to persuade Bielsa to go back on a decision he took in November to quit if an opposition ticket won the presidential election which it did.
"We want to inform you that the president of the ANFP continues in talks with the objective of Marcelo Bielsa carrying on," ANFP vice-president Mauricio Etcheberry told reporters.
Bielsa said the day before the November 4 election he could not work under opposition candidate Jorge Segovia.
The Spanish-born Segovia beat incumbent Harold Mayne-Nicholls, a FIFA official who had brought in the Argentine as coach in 2007, and Bielsa looked set to leave.
However, the result of that election 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, a 31-year-old lawyer, won a second election earlier this month and said he would hold talks with Bielsa after last weekend's friendly away to the United States which looked set to be the Argentine's last match in charge.
The 55-year-old Bielsa, extremely popular in Chile inside and outside of football, steered the country to their first World Cup since 1998 in South Africa last year. They reached the second round after which he signed a contract extension.
He won over Chileans, generally wary of Argentines, from all walks of live, notably business people, intellectuals and politicians, with his work ethic and scientific methods backed by good results on the pitch.
Shows of support for Bielsa became regular occurrences in Chile after his decision to quit and national team players have tried several times to get him to change his mind.
