ESPN.com's Alex Scarbrough reported this week that Hurts entered the transfer portal with an eye toward becoming a starting quarterback elsewhere.
Since Hurts already graduated, he will be eligible to play immediately if he transfers.
On Friday, the Washington Post's Emily Giambalvo tweeted a photo of Hurts visiting Maryland, which is coached by former Alabama offensive coordinator Mike Locksley.
AL.com's Michael Casagrande reported that Hurts also plans to visit Miami.
Oklahoma presents an intriguing option for Hurts since Kyler Murray is expected to enter the 2019 NFL draft, per Susan Slusser of the San Francisco Chronicle.
Austin Kendall was viewed as a strong candidate to take over as the Sooners' starting quarterback next season, but he also entered the transfer portal, according to ESPN.com's Jake Trotter.
Oklahoma quarterbacks have won the Heisman Trophy under head coach Lincoln Riley each of the past two seasons in the form of Baker Mayfield and Murray.
After leading Alabama to a 27-2 record in his two seasons as a starter, Hurts was replaced by Tua Tagovailoa this season.
Tagovailoa finished second in the Heisman Trophy voting, and Hurts saw only sporadic action behind him.
Hurts was productive when he played, completing 72.9 percent of his passes for 765 yards, eight touchdowns and two interceptions while rushing for 167 yards and two scores.
In his first two seasons, Hurts accounted for 61 total touchdowns and threw for just 10 interceptions, making him perhaps the most sought-after transfer in the country.
If Hurts does go to Oklahoma, he will have a legitimate chance to win another national title in his senior season given the Sooners' recent dominance over the Big 12 conference.