Last year, the Astros and Orioles agreed to a deal in principle that would have sent Britton to Houston, but the trade was called off after exchanging medicals.
Britton later tore his Achilles in December, but has since fully recovered and has looked especially sharp of late, allowing just three hits and no runs over his last eight appearances. Overall, he owns a 3.45 ERA, 1.34 WHIP, and 13 strikeouts in 15 2/3 innings this season.
The left-hander is set to hit free agency this winter and has approximately $4.6 million remaining on his deal for 2018.
Houston is believed to have plenty of competition for Britton. It was reported Saturday that the Chicago Cubs were deeply involved in discussions with the Orioles, while the Boston Red Sox, Atlanta Braves, Philadelphia Phillies, and New York Yankees have all reportedly been in contact with the Orioles.