But it seems there's no truth to the rumours. "The story is completely untrue," Katie's rep Leslie Sloane has confirmed. "The two have not spoken since she appeared on How I Met Your Mother."
Had the romance been true, Katie would have been the second Dawson's Creek alumni to date Jason, 34. He and Katie's co-star Michelle Williams were in a relationship for a year before splitting up in February 2013.
It has been 22 months since it was announced that Katie, 35, had filed for divorce from her husband of five years, Tom Cruise.
She now lives in New York with the couple's daughter Suri, and has managed to maintain a relatively low-profile while putting the focus back on her acting career.
Katie made a confident solo appearance in the Big Apple this week as she stepped out for Tiffany's 2014 Blue Book Gala. She looked fresh and flawless as she arrived at the Gugenheim Museum, wearing a simple Balenciaga mini with a white layered skirt.
She kept her makeup and jewellery to a minumum, and wore her hair in a chignon swept into a side fringe.