Thomas was supposed to work out for the team this week and Houston was reportedly expected to sign him, assuming the visit went well.
But the Texans called off the workout and have made no plans to reschedule it, sources told NFL Network's Tom Pelissero.
Thomas' agents cited Texans head coach Bill O'Brien in saying the NFL shut down the visit upon directing all teams to review their workout procedures amid the COVID-19 pandemic, according to ESPN's Adam Schefter.
The league issued its memo after the Tennessee Titans confirmed eight positive tests within their organization, forcing them to shut down their facilities and jeopardizing their availability for Week 4.
The Baltimore Ravens released Thomas before the season after he fought a teammate at practice. The 31-year-old was rumored to be an unpopular figure in the Ravens' locker room.
Houston had seemed like a logical landing spot for Thomas given its defensive struggles to begin the season. The Texans rank 29th in points allowed per game through three weeks and have yet to record an interception. The defending AFC South champions are 0-3 in 2020.
Thomas posted 49 tackles, two interceptions, and two sacks in 15 games with Baltimore in 2019. The seven-time Pro Bowler owns 30 career interceptions, catching his first 28 as a member of the Seattle Seahawks.