The "Horrible Bosses" star is said to have grown closer to the British beauty - who starred in his 2014 movie "Horrible Bosses 2" and can next be seen in Jason's Apple TV series "Ted Lasso" - following his November (20) split from longtime partner Olivia Wilde, whose romance with Harry Styles hit headlines just days after their break-up was made public.
"When Jason found out about his wife and Harry, Keeley was one of the people whom he turned towards," a source told Britain's The Sun newspaper. "During this time he was understandably devastated, but she was brilliant and incredibly supportive."
"He invited her to join him for a dinner with mates in Los Angeles, and their flirty banter quickly set tongues wagging. They have met up since, but obviously, it's all very early days. Jason feels it's too soon to leap into a new relationship - he is in absolutely no rush - but it's a case of 'watch this space.' "
Keeley first made a name for herself posing for The Sun's infamous Page Three, but stopped that gig in 2009 and moved to Los Angeles in 2012 to forge an acting career. She is thought to have struck up a friendship with Jason after starring as the assistant of Chris Pine's character Rex in the "Horrible Bosses" sequel.
She is said to have returned to London last year, when she apparently enjoyed a brief romance with comedian David Walliams. Keeley stars as Bex in "Ted Lasso", which also features a Page Three model called Keeley - played by Juno Temple.