The couple recently reunited following rumours that the footballer had cheated on Clancy while on a friend's stag weekend in Madrid.
The 24-year-old model reportedly underwent her 12-week scan at a London clinic yesterday and celebrated the news by going to lunch with Great British Hairdresser co-host James Brown.
A fellow diner at Italian eatery Strada told The Sun: "Abbey said she asked if a nurse could see a willy and she said she thought she could. Abbey also said she liked the name Johnny."
It is thought that Clancy phoned Crouch at the restaurant to reveal that they are having a baby boy.
Another customer added: "[Clancy] said, 'She's the expert. She said she could see what it is now which means it must be a boy. I reckon it's probably a boy. She said it's so perfect'."