"They're sweet on each other," a source close to the couple tells PEOPLE. "It's the beginning stages of a relationship." (His rep had no comment.)
What's the attraction? Friends point out that Lachey, 32, and Kardashian, 25 – who met at a party for Arizona Cardinals quarterback Matt Leinart last month – have at least one thing in common: failed marriages. Kardashian, whose father is the late O.J. Simpson trial attorney Robert Kardashian, divorced music producer Damon Thomas in 2004.
"Part of the attraction is they have both gone through similar life situations," says the source. "They developed a bond."
Still, Lachey may be going slow. "For Nick to settle down," says a pal, "it will take someone who is a lifelong partner."