"They and the whole family are delighted," Douglas Rossdale, Gavin's dad, told People.com.
Stefani's representatives were not immediately available for comment, the magazine said.
The couple married in London in September 2002 and are the parents of Kingston Rossdale, who is nearly 2.
"He is a great lad," Douglas Rossdale said of Kingston. "And we are very much looking forward to another grandchild."
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