The former X Factor USA judge rekindled her relationship with the British Formula 1 driver in January after they took a New Year's trip together.
The Sun reports that Scherzinger suggested she was hoping for a proposal from Hamilton, saying: "I would like to get married one day but it's not just up to me."
When asked about potentially having children, she added: "It would be nice."
The pair were spotted together last night (March 24) for the Malaysian Grand Prix.
The former Pussycat Dolls singer recently described Hamilton as a "very special" person.
She also recently said that her X Factor USA axe was down to Simon Cowell being "scared" of her.
> Lewis Hamilton: 'I'll be a cab driver when I retire from Formula 1'
Watch the video for Nicole Scherzinger's 'Try With Me' below: