The 27-year-old 'Mean Girls' star was delighted to learn Queen Elizabeth's granddaughter has moved to New York for her work with auction house Paddle 8 and has been bombarding her with invitations to hang out, reported E! online.
"Lindsay's long been obsessed with the royals, particularly Prince Harry, who she thinks is a perfect match for her," a source said.
"But Eugenie's quite low-key. The two run into each other at their favourite restaurants - La Cenita and bubby's - where Lindsay makes a beeline for Eugenie and invites her to her house," it added.
"She's practically stalking the princess in a desperate bid to upgrade her image," the source said.