Comedian Bailey, 58, was paired with pro dancer Mabuse, 33, for the 2020 series of Strictly and went on to win the series.
However, in an appearance on Loose Women on Wednesday, Bailey said that despite his star turn being three years ago he is still good friends with Mabuse.
Asked whether they were still close, he confirmed: "Oh yes."
Bailey added: "When she said she was having a baby, I said here's a couple of names for you - Bill, for a boy, obviously and Bailey if it's a girl.
"It makes perfect sense."
Mabuse, who has now left her role as a pro dancer on Strictly, announced the happy news that she and husband Marius Lepure are expecting their first child during an episode of Oti Mabuse's Breakfast Show in August.
She said: "Speaking of things that you didn't know at home, we have a little something for all of you, we've been holding some good news."
Lepure added: "Very good news, yeah. We're having a baby!"
While Bailey has recommended his name to his friend, he told Loose Women that his actual name is Mark and his own parents never really liked him being called Bill – a nickname he picked up from a teacher when he was at school.
Bailey said: "My parents never really got on board with it. My mum, she didn't like Bill as a name because Mark was my name.
"So when girlfriends used to phone up and ask for Bill, she'd say 'there's no Bill here' and put the phone down."
Bailey also showed viewers he could still dance parts of his Strictly routines as he got up to show a few steps from one of his most famous routines, his couple's choice to Rapper's Delight.
He said: "I just like generally dancing. But those moves, once they're in, they'll never leave."
Talking about growing close to Mabuse during Strictly, he said: "It was a strange time. We were in the Strictly bubble, but we were in an actual bubble because it was COVID. We didn't go out after training, we spent 12 hours training, then we would go home.
"After the big dance on Saturday night, there was no carousing."