The 40-year-old singer - who recently split from tennis player Grigor Dimitrov, 27 - was reportedly approached by former soccer star Jamie, 45, about going out on a date but rejected him in order to spend more time ''on herself and her career''.
A source told The Sun: ''Jamie has been very keen on Nicole but would never have tried it on when she was with Grigor.
''Since their split, he expressed an interest in dating her but the time isn't right for Nicole.
''She is on a break from Grigor and she deserves an amazing man, but she's focusing on herself and her career.
''They would make a lovely couple so who knows what will happen in the future.''
Former Pussycat Doll star Nicole started dating Grigor in 2015 but their romance recently fizzled out. Before Grigor, she had a long running on/off relationship with Lewis Hamilton.
Jamie and former wife Louise Redknapp, 44, divorced in 2018 after 19 years of marriage.
Meanwhile, Nicole has previously admitted that her ''greatest weakness'' is love.
The star believes she is a ''fool for love'' and says the ''bravest thing'' she has ever done is letting someone she loves go.
She said: ''My greatest weakness is - I'm a fool for love. A real sucker ... The bravest thing I've ever done is loving someone and letting them go when you know it's not healthy for you, or serving you. Then you're finally loving yourself.''
Despite her love fears, she has insisted she hopes to settle down and tie the knot in the future.
She said: ''I'd like to get married one day. I'm looking for a wedding, my wedding. I think the heavens will sing when I get married.''
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