Reuters reported that the draft bill had recommended a fine of US$1 million per day for any violation of the rule.
Facebook said it would launch the Libra cryptocurrency in next year through a new subsidiary Calibra which will also supply the digital wallet for the new currency.
The company said the wallet would be available in Messenger, WhatsApp and also as a standalone app, and that it would take steps to protect users' privacy.
The bill is likely to meet resistance from Republicans in the house and even if it passes the house, it would be difficult to get such a measure through the Senate.
US President Donald Trump has criticised the Facebook move and told firms which wanted to "become banks", that they should obtain a banking charger and conform to US and global rules for such activities.