The proposed law does not name BP, but would apply to any company that has experienced 10 or more deaths in the last seven years.
The April explosion of BP's Deepwater Horizon rig killed 11 workers.
Major blow
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According to the draft legislation, the deaths must have taken place at drilling, production facilities, or refineries, and must have broken US health and environment laws.
The Deepwater Horizon disaster is still being investigated.
BP has already accepted its guilt in a separate accident in Texas in 2005 that killed 15 people.
Although the proposal does not affect BP's existing US oil wells, if it became law it would be a major blow to the UK oil company, according to Evgenvy Solovyov, oil equity analyst at SG Securities. Read the full report here.
Source: BBC News, UK