The 'Smile' singer is said to have had her three-month scan recently, with the baby due this December.
Allen and her husband Sam Cooper already have a daughter, Ethel Mary, who was born last November and are thought to be over the moon.
"Lily has started telling her friends and everybody in her close circle is so excited for her," a source told The Mirror.
"It was a surprise but Lily and Sam are thrilled. The pair of them have loved every minute of parenthood so far and wanted to expand their brood quickly. So it's great timing."
25-year-old Allen has suffered two tragic miscarriages in the past, but doctors have apparently told the star that her current pregnancy is going well.
The singer reportedly confessed to friends she is surprised people hadn't guessed she was expecting again due to the size of her bump, especially after her guest appearance on stage with Professor Green at Manchester's Heaton Park last weekend.
"Lily was sure people were going to cotton on to the fact she had a pregnancy bump but she seemed to get away with it thanks to wearing very baggy clothing," a source said.
"Her bump has popped out very early – far earlier than the last pregnancy. She's been joking she feels six months pregnant already."
Allen recently tweeted that she was back in the studio after she finished work on the score for the forthcoming Bridget Jones musical.
Sources say she plans to continue recording this summer, before resting in the run-up to the birth.
Watch the video for Lily Allen's breakthrough hit 'Smile' below: