The 26-year-old actress is said to be "smitten" with the 50-year-old actor after hooking up with him in January while she was staying at Los Angeles' Chateau Marmont hotel while she filmed We Bought a Zoo with Matt Damon.
A source told the new issue of Us Weekly magazine:
"Their first hook-up was in Scarlett's Bungalow. She is smitten with him."
Scarlett - who split from husband Ryan Reynolds in December after two years of marriage - and Sean began their friendship when she was planning to fly out to Haiti to help people affected by the two earthquakes in January 2010.
The source added: "Scarlett first reached out to Sean when she was planning to visit Haiti with Oxfam. She knew Sean was living there in a tent and turned to him for advice."
Although she didn't end up going on the trip she and the Milk star - who is spending most of his free time on the Caribbean island, where he has been undertaking charity work since the disaster - are said to have developed feelings for each other.
Sean was previously married to Madonna, while his divorce from actress Robin Wright - mother of his two children Dylan, 19, and Hopper, 17 - was finalised in July after 14 years of marriage.
- BANG! Showbiz
