The Beatles legend, who is currently embroiled in a battle with estranged wife Heather Mills, regularly visits north London's Kenwood House art gallery to spend time looking at The Guitar Player - a 17th Century piece by Jan Vermeer.
A source said: "Paul is obsessed with the painting, which features a teenage girl strumming a guitar."
"He uses the gallery as a haven during his divorce from Heather. He often spends more than 40 minutes staring at The Guitar Player."
Paul has approached English Heritage, the owners of the painting, about buying the $100 million artwork but they have so far refused his offers.
Meanwhile, Rosanna Arquette's sibling Alexis Arquette has confirmed she is dating Paul.
The "Desperately Seeking Susan" star and the musician were spotted enjoying a romantic walk on London's Hampstead Heath last week and are getting close.
Alexis told People magazine: "They are spending more time together. They're good friends."
"Who knows, if something came out of it, that's cool, it's great."
Transsexual Alexis revealed that Paul, 65, and Rosanna, 48, met years ago and bonded over their love of music.
He said: "She interviewed him for a documentary she did on rock 'n' roll."
"She's been a big fan of his music for a long time, and I know they befriended each other several years ago."
Last week, it was revealed Paul had treated Rosanna to a gift of sexy lingerie and expensive perfume - the same present he uses to romance every woman.
A source said: "He has a ritual. He buys the same thing. He's been buying a bottle of perfume and lingerie for so long, it's predictable."
"He gives it to them even before they get dinner. He's done it with everyone he's been with."
