Katie has remained a free agent since divorcing Tom Cruise in 2012.
She and Jamie raised eyebrows after they were spotted dancing together at an event in the East Hamptons in August 2013.
That same summer, Jamie brushed aside talk of a romance and was quoted by ibtimes.com as saying: 'In fact, it's quite hilarious because we simply danced at a charity event along with a lot of other people.'
Katie and Jamie were also seen acting cosy together with arms linked at a Super Bowl party in February of last year.
One reason why Jamie might be so 'Mission Impossible' about the relationship is his friendship and respect for Tom Cruise, with whom he starred in Collateral in 2004.
Cruise raved about Foxx when his former co-star picked up the MTV Generation Award at the 2013 MTV Movie Awards.
'I love Jamie. First of all, he's just an amazing human being, just so multi-talented,' Tom said.
In an interview with People last November, Katie expressed her desire to find love again.
'I'm a very loving person. Of course I'm open to finding love again,' she said.
Katie, meanwhile, is enjoying a new role on the Showtime series Ray Donovan that is being shot in LA.
The mother-of-one has been soaking the sunny California weather with her little girl on occasion, as they did during a trip to the shopping mall on Monday.
- Daily Mail