A source told the News Of The World: "Lindsay’s had her eye on the Dakota building for years. It's an iconic building and she plans to make it a hotbed for parties."
John Lennon, who had a home in the apartment block, was killed on the entrance steps in 1980.
Meanwhile, it has been reported that Lohan's dad Mike has banned Ronson, 31, from attending his forthcoming wedding.
Earlier this month, a spokesperson for Lohan quashed rumours that the couple are planning to raise a child together.