According to ESPN's Todd Archer, Prescott said:
"My fire is burning and my fire is big. You can throw whatever you want in there for it to burn and for it to get bigger. I don't know if I'm necessarily trying to prove something to the Cowboys or to this team because I feel like everybody in this building, this organization knows the player I am, knows the man that I am, knows where my heart stands.
"I just want to be great."
While Prescott and the Cowboys didn't come to terms on an extension, he will make big money this season, as the franchise tag will pay him over $31.4 million.
Prescott could hit the open market as a free agent following the 2020 campaign, and another big statistical season in 2020 would go a long way toward helping him become one of the NFL's highest-paid quarterbacks, whether with the Cowboys or another team.
Prescott was a fourth-round pick in the 2016 NFL draft, but when then-Cowboys starting quarterback Tony Romo got injured during the preseason, he took over and never looked back.
Over four NFL seasons, he has started all 64 games for the Cowboys and posted a 40-24 record with two NFC East titles.
Prescott is also a two-time Pro Bowler. While he didn't make the Pro Bowl last season, he enjoyed the best statistical year of his career, completing 65.1 percent of his passes for a career-high 4,902 yards and 30 touchdowns against 11 interceptions. He also rushed for three touchdowns, giving him 21 rushing scores in his career.
As good as Prescott was last year, he could be even better in 2020 thanks to the talent around him. The Cowboys added first-round pick CeeDee Lamb to a receiving corps that includes Amari Cooper and Michael Gallup. Running back Ezekiel Elliott returns as the starter, and tight end Blake Jarwin should have a bigger role.
The possibility of a massive contract could loom large in the mind of some players, but Prescott insisted he is focused on controlling only what he can control: "I seize the moment. I focus on the now. I think it's very important for me to do exactly that and not to be distracted or put too much focus anywhere other than what it is that I'm doing now."
If Prescott matches or exceeds what he did last season, the contract situation should resolve itself. The Cowboys should also do much better than the 8-8 record they posted last season.
Dallas is favored to win the NFC East in 2020 primarily because of the firepower it has on offense.
Prescott's first chance to impress in 2020 will come Sunday night when the Cowboys face the Los Angeles Rams at SoFi Stadium in Inglewood, California.