The 'Shout' star is among the 14 celebrities competing in the new series of the BBC competition. On Saturday's launch show, viewers saw Lulu's surprised reaction as Sir Bruce Forsyth and Tess Daly announced that she would be dancing with Cole.
However, The Sun claims that the 62-year-old did not want to dance with Cole, and had hoped to be paired with newcomer Pasha Kovalev.
"I was in shock," Lulu said. "I want to stay in the show as long as I can because I want to learn to dance. I am good for a few moves but I am not a dancer."
An insider told the paper: "She'd been telling people - including Brendan - at rehearsals that she really didn't want him. Brendan has a reputation for being really strict with dance partners and a hard task-master.
"She wanted someone who'd be softer with her - and had set her sights on Pasha."
Cole admitted that he decided to lift Lulu over his shoulder after seeing her reaction: "I had to get over the shock of being rejected so harshly.
"I'm the tallest dancer and she is the shortest celebrity. You know when you look around the group and think, 'She's fantastic', height-wise and look-wise.
"We both looked at each other and thought, 'It's never going to happen'. Once we get over the initial shock, I'm sure it will be fine."
> 'Strictly Come Dancing' Lulu 'astonished' by partner
Watch the new Strictly Come Dancing trailer: