"They have a lot in common. Caitlin plays music and John loves music," a source tells PEOPLE of the new couple, who were spotted on an adorable ice cream date this week.
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"She is a really sweet person. They're dating, but it's not serious yet," says the source.
McHugh has showed off some of her skills on her Instagram account.
On The View last week, Stamos spilled the beans that he was dating someone while discussing his work with the Beach Boys.
"This girl I'm dating … she loves this song, 'Disney Girls,' " the actor said. "So I put on FaceTime. … I thought I could get away with [it] but people were tweeting, 'Who are you FaceTiming?!' "
Stamos' Fuller House season 1 is streaming on Netflix now, and Grandfathered airs Tuesday at 8:30 p.m. ET on Fox.