The New York Post reported that the outfielder was offered an eight-year, $200 million extension offer following the 2017 season -- a season in which he hit .264 with 24 homers and 102 runs batted in.
He followed up that 2017 season with an even better 2018, in which he won the AL MVP award, hitting a league-high .346 with 32 home runs and 80 RBI, as well as 30 stolen bases.
Betts told MLB.com on Wednesday that he does not expect to ink a new deal with the Red Sox anytime soon.
"That's exactly what I expect. I don't expect anything to happen until I'm a free agent," Betts said.
"It's just one of those things where you've just got to go out and play, you can't worry about the economics of the game right now. [The Red Sox] have to take care of what they have to take care of, and I have to take care of what I have to take care of. The common thing is to win a World Series, and I think it's something we definitely both want to do."
Betts is eligible for free agency following the 2020 season, and at that time he will be just 28 years old and a prime candidate for a huge contract once he hits the open market.
The outfielder made $10.5 million last season, and avoided arbitration with the Red Sox by agreeing to a $20 million deal for the 2019 campaign.
"I'm under no pressure to do anything," Betts told the Boston Herald.
"It's OK for two sides to disagree. It's perfectly fine. It's a normal thing. I've got two more years. I'm going to make the best of them. I have to work on Year 1 right here. I'm going out to do my best to help the team win, also next year. It's all right to disagree."
The rejection of the deal for Betts comes following a couple of massive deals recently inked by big-name players around Major League Baseball, including the Los Angeles Angels' Mike Trout, who on Tuesday agreed to a 12-year, $430 million contract extension.