A baby brother or sister for Prince George could arrive sooner than expected.
However, Kate is said to be keen to grow her family and has hinted she wants more than one more child in the future.
"Kate has been talking about having at least three children, which is why she is keen to be pregnant again," a source told the newspaper.
"The Duke would probably be happy with two but Kate is very close to her brother and sister and there is a sense that as she is one of three, she would like to have three herself."
The baby news comes after it was revealed Prince William and Kate are loving country life at their Grade II listed Norfolk mansion.
"Kate and William are country folk at heart. While their London home will be their base in terms of royal duties, Norfolk is where they want to bring up their family," a royal source told Grazia magazine.
"The couple will get another dog and hope to have another baby while there," the source added. "It's very sociable in the area and Kate really loves the Norfolk lifestyle."
Meanwhile, Kate will have to wave goodbye to her one-year-old son George when she heads off on her first solo Royal Tour next month.
The duchess will fly to Malta on 20 September to celebrate the former British colony's 50th anniversary of independence.
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