The 28-year-old has been in a relationship with the American singer, who is currently filming as a judge for the new UK series of The X Factor, for almost six years.
"We've been together for five years, which is quite a milestone really," The Sun quotes Hamilton as saying. "But hopefully [I'll propose] in the near future. Maybe before we get to six years."
Hamilton is preparing for the British Grand Prix at Silverstone this Sunday.