Stormy Daniels told CBS News' 60 Minutes programme that a man approached her in a Las Vegas car park in 2011.
The stranger allegedly said "leave Trump alone", then looked at her young daughter and added: "It'd be a shame if something happened to her mom."
Mr Trump denies having had an affair with the actress.
His lawyers are seeking $20m (£14m) in damages from her, saying she broke a non-disclosure deal signed before the 2016 presidential election.
She has filed a lawsuit to scrap the agreement, saying it is invalid because Mr Trump did not sign it.