The person, who requested anonymity because of the sensitive nature of the relationship, said the couple had differing lifestyles, but that Parker holds Morgan in the highest regard and hopes they remain friends.
Morgan, best known for his recurring role as Denny on “Grey’s Anatomy” and the deceased husband of Parker’s character on “Weeds,” began dating Parker in 2006. The pair briefly split last June but later reconciled. Parker, 43, and Morgan, 41, announced their engagement earlier this year.
Representatives for Parker said they do not comment publicly on the personal lives of clients.
In 2003, a tabloid frenzy ignited when actor Billy Crudup left Parker while she was seven months pregnant with their son, then began dating Claire Danes. Parker and Crudup had been together since 1996.
Parker has previously been romantically linked to Counting Crows lead singer Adam Duritz and actor Timothy Hutton.
The fourth season of “Weeds” premieres June 16.
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