The Manchester United youngster - who enjoyed a breakthrough season for his boyhood club with 17 goals in all competitions during the last campaign - has been selected for his country's Nations League fixtures in Iceland and Denmark.
He's quoted by BBC Sport as saying: "Obviously any young football player would want to break records. And if you didn't, there's something wrong.
"It's always nice to have visions and goals you set in your football career and that goes for virtually any England forward.
"Just go out there and do your best and break records and just be remembered forever, really."
The 18-year-old star's 17 goals last season puts him level with United legends George Best, Brian Kidd and Wayne Rooney, with no teenager scoring more in a single campaign for the Red Devils.
And Alan Shearer - who holds the all-time Premier League record of 260 goals - has backed Greenwood to surpass him.
The young footballer added: "The games have come so quick and you have to be focused 100% at all times. My whole family was excited for me and it's a dream come true.
"It's happened quick. You can be called on at any time and I got called in for some Europa League games early in the season and took my chances and took every game as it came and just played my football."