09/12/2014 10:04 EDT | Updated 11/12/2014 05:59 EST

Neil Young reportedly dating Daryl Hannah 'for months'

Neil Young and Daryl Hannah are rumoured to be a hot new celebrity couple, one month after the veteran Canadian rocker announced his split from his wife of 36 years.

Paparazzi captured Young and the Kill Bill actor getting cozy at Sur La Table​ in Westlake, Calif., on Tuesday. Unnamed sources told People magazine that the pair has been "dating for months."

The 68-year-old musician and the 53-year-old actor-turned-activist have known each other for years.

The pair have appeared separately at a number of recent environmental protests, and collaborated on a Greenpeace documentary on the Alberta oilsands earlier this year.

Young stunned the music world in August when he announced his split from his longtime wife, and musical collaborator, Pegi Young. The two wed in 1978, and have two adult children together— a daughter and a son who has cerebral palsy.

Their son's condition inspired them to co-found The Bridge School in 1986 to help educate children born with severe physical disabilities.

A hearing on the divorce filing is scheduled for Dec. 12, according to the San Mateo, Calif., court website.