The couple are thought to have started dating in May but In Touch Weekly claims that they are no longer together.
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"They're very different people," a source explained.
Davis is said to be "focused" on raising her daughter Gemma, whom she adopted last year.
Meanwhile, Sorkin is reportedly busy working on his HBO series The Newsroom, which has been renewed for a second season.
However, the insider claimed that the split between Sorkin and Davis was amicable, saying: "They'll definitely remain friends."
