They became close and Hucknall attempted to woo the actress by taking a bath with her during one encounter - but Nielsen insists she would never have slept with the singer "even if you'd paid me".
In her upcoming autobiography You Only Get One Life, serialised in Britain's The Sun, she writes, "Now I was single, I had a chance to meet a completely different type of man - like Simply Red singer Mick Hucknall.
"I was working in Manchester and we ended up going back to his place. It was very much the laid-back musician's pad - all warm colors, joints going around and candles. At 3am Mick said: 'I'm going to have a bath - do you want to join me?' 'I'd love to!' I said, thinking, 'This is weird' but at least it was a variation on being asked to go to bed. He lit more candles in his purple bathroom, put some music on, then we were in the water.
"Now Mick is many things but one thing he's not is a very good-looking guy. However what he does have is this expression of someone who knows he's totally outrageous and yet very friendly, really cool.
"So I was just winging it and there we were, taking a bath together. We talked about ourselves and nothing happened. To be honest, even if you'd paid me I couldn't have gone to bed with the guy."
Hucknall has previously dated actresses Catherine Zeta-Jones and Martine McCutcheon, as well as supermodel Helena Christensen, but wed girlfriend Gabriella Wesberry last year (10).