Last month, CONMEBOL asked FIFA to delay the start of the qualification campaign as the first two rounds of matches at the end of March could not be played due to football being suspended on the continent over the deadly virus.
"For the moment, the start fixed by (FIFA) for its celebration is September 4-8 in the format already established," said CONMEBOL.
All 10 teams are due to play each other home and away in a round robin format.
That amounts to 18 matches, far more than most other continental federations organize.
The first two rounds need to be rearranged but CONMEBOL said any new dates would have to be ratified by FIFA.
And with the Copa America being postponed until next year, the opportunities to fit in an extra two rounds of matches appear few.
As it is, two rounds of World Cup qualifiers are due to be played on June 3 and 8, 2021, with the Copa now set to begin on June 11.
Meanwhile, CONMEBOL said that no restart date could yet be fixed for its flagship club competitions, the Copa Libertadores and Copa Sudamericana.
However, it reiterated its "determination" to complete the 2020 editions of both tournaments -- the South American equivalents of the UEFA Champions League and Europa League.
During a video conference meeting with the presidents of its member associations, CONMEBOL insisted that "the priority remains preserving the health of the great South American football family."