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The 42-year-old actor, who has a nine-year-old daughter with his ex-wife, Courteney Cox, and his on-again/off-again girlfriend, Christina McLarty, are reportedly expecting their first child.
Sources told gossip website TMZ.com that the Entertainment Tonight host, who has been dating the David for two years, is four months pregnant.
David also gushed about the good news to the crew on the set of his new movie in Vancouver, Canada.
A spokesperson for the actor has yet to comment on the reports.
David, who admitted last week that he had fallen off the wagon after seeking treatment in rehab for alcohol addiction, previously hailed Christina to be the love of his life.
He said: "I'm madly in love with her and she's the love of my life. Absolutely."
The actor split from former Friends star Courteney in 2010 after 11 years of marriage but they are still close, and he recently gushed about his relationship with their daughter.
He said: "She's the most brilliant, beautiful friend that I've ever met."
