"It would mean a lot," said Chubb, who said that his agent and the team have already discussed a potential extension this offseason. "Cleveland drafted me and trusted me and put their faith in me to help build this culture and this team I'm a part of. Cleveland is where I want to be. Hopefully everything can work out in that direction."
Chubb, a second-round pick in 2018, has been the backbone of the Browns' offense the past two seasons, averaging 5.25 yards per carry during that span.
In 2019, he came within 47 yards of besting Tennessee Titans running back Derrick Henry for the rushing title. Last season, Chubb missed four games because of a knee injury but still finished seventh in the league with 1,070 yards on the ground, as Cleveland made the playoffs for the first time since 2002.
Chubb has been especially efficient late in games. Last season, he led the NFL with an average of more than 10 yards per carry in the fourth quarter.
Chubb said that his supporting cast -- which includes one of the top offensive lines in the league -- as well as coach Kevin Stefanski's run-heavy offense are among the reasons he prefers to stay in Cleveland.
"I don't like uncertainty," Chubb said. "I know here in Cleveland what I have, the players and coaches and the city of Cleveland. Cleveland is where I want to be. That's my main focus."
Last summer, the Browns extended Chubb's backfield sidekick Kareem Hunt to a two-year extension worth $13.25 million, keeping Hunt under contract in Cleveland through the 2022 season.
The Browns, who are holding their mandatory minicamp this week, have two other key players they drafted in 2018 who are extension-eligible this summer in quarterback Baker Mayfield and cornerback Denzel Ward. Cleveland has already picked up the fifth-year options on Mayfield and Ward, which will keep them under contract at least through the 2022 season.
Ward, a Pro Bowl performer in 2018, said Tuesday that his agent and the Browns have begun talking about an extension as well.
"In a perfect world," Ward said, "I'd definitely want to be a Brown for the rest of my career."