The 30-year-old beauty, who shares daughter LILA GRACE with magazine publisher Hack, was spotted departing for a romantic weekend in New York on Thursday (1APR04) with hunky Craig, who teamed up with her pal Gwyneth Paltrow in 2003 flop Sylvia.
And sources close to Moss say the relationship, which begun a month ago when they were introduced by mutual friends, is already very serious. And many predict Craig may be the man to tame wild woman Kate.
A close pal tells the SUNDAY MIRROR, "It was love at first sight for Kate. Daniel is bright, charming and leads a very low-key life - just what Kate's looking for at the moment.
"It's serious and they both know it. Kate doesn't want anything to rock the boat. She is blown away by him. Only her closest friends were in on the secret. They all think he's utterly gorgeous."