Hilton met McCartney at a Grammy post bash, and expressed her wish to record a duet with him.
"I'd love to do a duet with you. I'm a singer too and have had an album out," the Sun quoted her as saying.
But McCartney, who seemed baffled for a moment, politely declined her request.
"Sir Paul was minding his own business when Paris traipsed right up to him and introduced herself. He looked bemused, smiled and nodded - then stumbled out that he'd have to check his schedule," a source said.
The source further revealed that Hilton later complimented McCartney on his hair.
"It's just like in The Beatles. It's so cute," she said, according to the source.
While McCartney is a legendary musician, Hilton released an album in 2006, which was badly panned by the critics.
Read more about: Paris Hilton at the Grammys
