Dow Jones quoted analyst firm Jefferies saying it would require a lengthy evidence-gathering process to get the ban through U.S. courts.
The mooted ban, which could take up to two years to take effect, would be a massive blow for manufacturers of menthols such as British American Tobacco (BAT) and Imperial Brands.
It also highlights that despite the move towards vapour and heated-tobacco products, BAT is still heavily reliant on its cigarettes business.
"Menthol will make you inhale more".
Steadily declining numbers of smokers paired with an increasingly hostile regulatory environment for tobacco products have troubled shareholders for some time now.
BAT shares have dropped 40 percent this year, the biggest drop in at least two decades.
A previous study also found that a huge percentage of African-Americans are addicted to traditional menthol cigarettes.
British American Tobacco fell 9% to £30.15 while Imperial Brands declined 3.8% to £36.44 on the speculation. The Winston maker gets about 15% of earnings from menthol brands such as Kool and Salem in the United States, according to Jefferies.