Hameed became the first Lancashire player ever to score two centuries in a Roses match in this week's County Championship draw with Yorkshire.
It also made the 19-year-old the youngest player to hit two hundreds in an English first-class game.
"I've never tried to hide away from the fact I want to play for England - the sooner the better of course," he said.
The former England Under-19 captain told BBC Radio Lancashire: "I realise the thing that will get me there is putting in performances for Lancashire consistently and that is my sole focus for now."
Hameed has only played 16 first-class matches after making his debut last season, but his 114 and 100 not out against Yorkshire took him past 1,000 runs for the season in his first full campaign.
When asked about Lancashire head coach and cricket director Ashley Giles comparing him to Joe Root, Hameed said: "That's special, being linked to one of my role models in the modern day.
"He's unbelievable in all three formats and I've mentioned before that I want to be like him in the future where you can play all three formats consistently."
Teenage opener Haseeb Hameed hopes his recent Lancashire form is attracting the attention of England's selectors.