The chart-topping group are currently filming their movie debut opposite Lohan in the comedy Just My Luck, which is set for a 2006 release.
The pair apparently began "mucking around together on set" and have since been on a few dates together.
The rumours appear to emanate from the blog posting of one LA partygoer last week, who claimed that Harry and Lindsay were heard enjoying "a clandestine f***" together in a bathroom.
