Alex Speier of the Boston Globe previously wrote that the two are nearing a deal to keep Sale with the reigning World Series champions "for years to come."
The left-hander, who turns 30 on March 30, would become the latest superstar to re-sign with his current team before potentially hitting free agency. The group already includes the Los Angeles Angels' Mike Trout and St. Louis Cardinals' Paul Goldschmidt.
Sale is set to enter the final season of a five-year, $32.5 million contract. He's scheduled to make $15 million in 2019 before potentially hitting the open market next offseason.
An extension would alleviate concerns the Red Sox could lose one of the most important members of their star-studded roster next winter.
Sale, who started his career with the Chicago White Sox before getting traded to Boston in December 2016, earned his seventh consecutive All-Star selection in 2018 while posting a microscopic 2.11 ERA with 237 strikeouts in 158 innings across 27 starts.
Sale dealt with shoulder inflammation during the second half of the 2018 campaign, but told Christopher Smith of MassLive in January there were no lingering concerns.
"Obviously I feel normal again," he said. "Being able to throw free and easy and feel loose...obviously is a nice feeling. So we're just kind of building up like a normal offseason, getting ready for spring training."