The 'Greatest Day' singer has reportedly been romancing the former 'Doctor Who' star since meeting her when they filmed a charity TV sketch for Comic Relief in March, during which she impersonated him.
They have been on dates including an overnight stay in Stratford - the birthplace of William Shakespeare where they watched a production of his play 'A Midsummer Night's Dream'.
A friend told The Sun newspaper: "It's a very unlikely pairing but they have really hit it off.
"They've been on a number of dates to the theatre and the cinema. They really enjoy each other's company.
"Catherine deserves someone nice and she has landed on her feet with Jason. But they have both been desperate to keep their romance secret."
Jason, 41, and Catherine, 43, have also lunched together in Stratford, Central England, but arrived separately to avoid being spotted.
An onlooker said: "They were trying to keep things secret but looked very loved up and happy together."
The couple met when Catherine starred as spoof band Fake That, portraying Jason alongside British comedians James Corden, Alan Carr, Kevin Bishop and David Walliams. The real group - Jason, Howard Donald, Gary Barlow, Mark Owen and Robbie Williams - also appeared in the sketch.
Jason and Catherine are said to have kept in touch after filming and get together after she split from partner Twig Clark this summer.
Jason has never married, but previously been linked to a number of beauties including topless model Kathy Lloyd, singer Lulu and TV star Jenny Powell.