According to multiple reports, the two sides are not engaged in negotiations at this time.
Clowney, by rule, would earn the $15.967 million one-year tender value for 2019 if he doesn't sign a new deal by 4 p.m. ET Monday.
Houston's front office is operating without a general manager, but the Texans have shown no signs of progress in negotiations with Clowney for months.
Without a deal in place, Clowney is not expected to participate in training camp and could opt to stay away from the team until September, returning in time to avoid fines and prepare for Week 1 of the regular season.
The 26-year-old pass rusher was named to each of the past three Pro Bowls, tallying 53 tackles for loss over that period. He has 29 sacks since the Texans made him the No. 1 overall pick in 2014.
Prior to the draft, there were rumblings Clowney could be available via trade, but Clowney's camp has said he did not request a trade out of Houston.
--Field Level Media