Kelsey Grammer has a possibly pregnant new girlfriend?

Kelsey Grammer -- in the midst of a divorce from his third wife -- has a new blonde British girlfriend.

They've already been photographed -- wearing matchy-matchy sportswear -- holding hands in New York, where he's living and starring in "La Cage aux Folles" on Broadway.

All we know is that her name is Kate and she may be pregnant. If it's true, this will be the second time the "Frasier" star has started a new family while married. His 18-year-old daughter was conceived with a hairdresser during his marriage to second spouse Leigh Anne-Cushany.

Oh, and he has three other kids, two (ages eight and five) with Camille Donatacci  and one ("Greek" star Spencer Grammer, age 26) from his first marriage.

Camille -- his third wife -- filed for divorce in July and at the time Kelsey denied there was another woman, revealing on his Twitter that the break had been a long time coming and begging fans and followers not to condemn Camille.

"Camille and I had been discussing the possibility of a separation for some time before all this happened. She finally decided she should file. I respect her for this decision ... I hope to have a great partnership with her in the raising of our children. 

According to Page Six, "He's pushing for a quickie divorce because things are moving quickly with his new girlfriend. There is speculation that she is pregnant, but he wants to finalize the divorce before making any announcement."

A rep for Grammer confirms the new relationship, "They are very happy together." On the possible pregnancy, "Kelsey did not discuss it with me."

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