The Four Weddings and a Funeral star split from her French husband Francois Olivennes - the father of her three children - in 2005 after 18 years together.
The 49 year old reportedly enjoyed a brief fling with English actor Tobias Menzies, who is 14 years her junior, following the breakdown of her marriage, but has been single since.
But now, she is stepping out with Barron - the man behind Michael Jackson's Billie Jean video - according to Britain's Daily Mail newspaper.
A source tells the publication, "Steve and Kristin met through mutual friends in the film industry eight months ago and have been inseparable ever since. Now there are murmurs that they are trying to work on a project together."