The 28-year-old, who will line up for Mercedes this season after leaving McLaren, has been known to record his own tracks as a hobby.
"He's working on some music and I'm working on some music," former Pussycat Dolls singer Scherzinger told Capital FM. "We're gonna harmonise, become as one.
"It sounds amazing. Everybody's free to do music or something, a hobby or what they love, so I do nothing but support him."
Hamilton reportedly spent time in a music studio collaborating with British rapper Angel.