The pair met in the early '70s, Andersen wrote, according to an extract printed in the New York Daily News, and became fascinated with one another, attending each other's concerts and sending gifts.
Their relationship quickly turned physical, he wrote.
"It was the glitter era, and everybody wanted to be part of the bisexual revolution," Andersen quotes singer Chuckie Starr as saying.
"(Bowie's wife) Angie even reportedly arrived back at her and Bowie's London home one day to find the two in bed together, Andersen wrote, the Daily Mail reported.
"Angie went upstairs to her bedroom, slowly pushed the door open, and there they were: Mick Jagger and David Bowie, naked in bed together, sleeping.
"Both men woke up with a start. 'Oh, hello,' said Bowie, clearly taken by surprise. 'How are you?'
"I'm fine," Angie replied. "Do you want some coffee?"
Angie reportedly "felt absolutely dead certain that they'd been screwing. It was so obvious, in fact, that I never even considered the possibility that they hadn't been screwing."
Bowie has previously been open about his and wife Angie's bisexual extra-marital love-life.
- AAP