Astros owner Jim Crane confirmed earlier Friday that talks with the former American League MVP were ongoing, and set Sunday - the end of camp - as a deadline to reach a deal.
Verlander, 36, joined the Astros via trade near the end of the 2017 season. After helping them win that year's World Series, he turned in one of the finest campaigns of his career in 2018 and was the runner-up for the AL Cy Young Award.
He's currently in the final year of a seven-year, $180-million contract signed in 2013 while still a member of the Detroit Tigers.
If the Verlander extension is completed, it will mark the third such contract for a Houston player this spring. The team locked up reliever Ryan Pressly on a two-year deal, and third baseman Alex Bregman on a five-year, $100-million pact officially announced on Friday.