The four-times overall World Cup champion sent a letter to men's race director Gunter Hujara, asking him about the possibility of competing in the men's downhill at Lake Louise, Alberta, where the first speed events of the season are taking place.
At this time, the women will be in Aspen, Colorado, racing a slalom and giant slalom.
Hujara and the Alpine Board considered the matter in Zurich this week during the FIS Autumn Meetings.
"We have been talking about it but no decision has been taken yet, it's a matter that the FIS Council has to examine during its next meeting in November," said Norway's Atle Skaardal, the women's World Cup race director.
"It's necessary to go through the rules to see if there is a way to do this and also a reason to do it.
"It's complicated because no racer is supposed to ski on a race course a week prior to his or her own competition. If Lindsey Vonn could train and compete with the men in November, she would have a huge advantage on her rivals the following week during the women's races on the same course," Skaardal added.
The winner of 53 World Cup events in her career including 26 downhills, Vonn is the second most successful women's downhill specialist behind Austria's Annemarie Moser-Proell, who won 36 downhills between 1970 and 1980.
Last year, the American also became only the fourth woman to triumph in all five disciplines of modern alpine ski racing: downhill, slalom, giant slalom, Super-G and combined.
She narrowly failed to break the benchmark of 2,000 points set by Austria's Hermann Maier in the 2000 World Cup, scoring 1,980 points to win her fourth overall crystal globe.
Experts believe the 2010 Olympic champion may lose as much as five seconds to the fastest men.