“Sources say the couple of nearly two years are planning to move in together and are looking for apartments downtown,” reports New York Post.
It’s not known when the pair are hoping to move in together or if they have a set idea about the kind of property they want.
Jessica and Stavros were first linked in December 2010, after they were spotted enjoying an evening at a nightspot.
“The Sports Illustrated model and the Greek shipping heir were canoodling at 1OAK on Wednesday, a spy said, and eventually left together,” it was claimed at the time.
Jessica had previously been in a long-term relationship with Nicolas Potts from the band Tamarama, while Stavros has dated Paris Hilton.