Sean Ono Lennon, 42, and James McCartney, 40, appeared in the photo together Monday on Instagram.
The picture shows Lennon and McCartney peering at the camera as McCartney holds a guitar. The pair didn't share further details about their meeting.
"Peekaboo..." Lennon captioned the post.
Lennon is the son of John Lennon, who died at age 40 in 1980, and Yoko Ono, and the brother of Julian Lennon, John Lennon's son with first wife Cynthia. McCartney is the only son of Paul McCartney and Linda McCartney. Fans encouraged the pair to collaborate in the comments.
"Wish you two would get together and do a tour," one person wrote.
"This is so cool!! Two sons of two amazing musicians! I hope you going to work together!" another added.
McCartney previously told the BBC he'd be open to working with Lennon and other children of former Beatles members.
"I'd be up for it. Sean seemed to be into it, Dhani seemed to be into it," he said, referencing George Harrison's son, Dhani Harrison. "I'd be happy to do it."