Reed, who has spent his entire career with the Baltimore Ravens, visited the Texans last week but left last Friday without a deal.
According to reports, the Texans offered Reed a 3-year deal in the salary range of $4 million per year, though Reed has been seeking a salary similar to the $7.2 million he earned last season.
The Ravens, who have seen significant turnover since winning the franchise's second Super Bowl, appeared interested in retaining the nine-time Pro Bowler.
"On the hopeful scale I'd say it's of high hope," Ravens coach John Harbaugh said at the NFL owners meetings Tuesday. "It's high on the measuring stick. We'll just have to see how it works out."
Reed, 34, is the Ravens' franchise leader in interceptions with 61, and his 1,541 return yards with those pickoffs is an NFL career record. He was the NFL's top defensive player in 2004.
With Reed possibly on the move, Baltimore has also scheduled a visit with Raiders free-agent safety Michael Huff, a league sourced told Schefter.
ESPN.com's Jamison Hensley and The Associated Press contributed to this report.