The Jets have not expressed any official interest in extending Adams' contract thus far in the offseason, the source said. The team entertained offers for Adams at last year's trade deadline.
The NFL and players' union reached agreement earlier this week on details of a virtual offseason for teams and players in the wake of the coronavirus pandemic. Teams with new coaches can start contacting players on Monday, and teams with returning coaches can start their programs on April 27.
Were the Jets to extend Adams, it would be a rare move. Under the current collective bargaining agreement, 15 of 191 first-round picks from 2011 through 2016 received extensions after their third season. That 15 includes only four defensive players -- defensive linemen J.J. Watt and Robert Quinn, linebacker Luke Kuechly and cornerback Patrick Peterson.
Adams, 24, is scheduled to make $3.5 million in 2020, the final year of a four-year contract that averages $5.6 million annually -- 23rd among safeties, per overthecap.com. As the No. 6 overall pick in 2017, his contract was fully guaranteed for $22.3 million, which ranks fifth at his position.
ESPN's Rich Cimini contributed to this report.