In a Face Time conversation with Sunak, the striker said his ambition was to beat Alan Shearer's 260 Premier League goals, with the Tottenham Hotspur player currently on 204.
Only Shearer and Rooney (208) have scored more goals in the competition's history.
"Yeah it's definitely there. I'm getting closer, so it's for sure something I want to achieve," Kane told Sunak, who congratulated the 29-year-old striker on achieving his England record in a call released on Twitter on Saturday.