Nenad Lalovic, the acting president of FILA, told The Associated Press on Wednesday that a rules committee will recommend the move - which would also eliminate a weight class in both men's freestyle and Greco-Roman - during the organization's congress in Moscow next week.
Wrestling officials would then include the change in their May 29 presentation to the International Olympic Committee for provisional status in the 2020 Olympic Games.
The IOC recommended in February that wrestling be removed from the Olympics after the 2016 Games in Brazil.
There were seven weight classes for men's freestyle and Greco-Roman at the recent London Games and four for freestyle women. Lalovic said the six proposed weight classes for women would likely fall between 50 and 74 kilograms.
"Women's wrestling today is very spectacular. Very interesting to watch," Lalovic said. "Why shouldn't we be representative of women as well as men?"
FILA spokesman Bob Condron said it's not clear which men's weight classes might be cut to make way for an expanded women's program.
Lalovic, a Serbian who is expected to be elected as FILA's permanent president next week, also said FILA's constitution is currently being tweaked to give women a more active role in the organization. He said he plans to insist upon adding a female vice-president to the governing body, and that a female commission is set to be formed as well.
"Women have become very important in our sport as athletes. But they also have to be important as administrators," Lalovic said.
If the change from four to six women's weight classes is approved, it could open up a discipline that's been dominated by Japan since its inclusion in the Olympics in 2004. The Japanese claimed three of the four gold medals awarded in London after winning two each in Beijing in 2008 and at the Athens Olympics four years earlier.