The newspaper said the baby is due to be born in December.
She "has started telling her friends, and everybody in her close circle is so excited for her," a friend told the Mirror.
"Thank you for all your congratulations today. I honestly couldn't be happier. such an honor to be on the list!#Timestop50tweeters," Allen said via Twitter.
Allen, who married businessman Sam Cooper last summer, was pregnant two other times, but suffered miscarriages.