The Astros will have to significantly lower their asking price, according to sources. But the Orioles remain interested because Norris, 28, is making only $3 million this season and is under team control through 2015. And he's posted a 3.93 ERA this season on a bad team.
One concern beyond the Astros' demands for multiple top prospects and more: Left-handers are batting .306 against Norris this season, which is why manager Buck Showalter had eight left-handed hitters in his lineup before Lucas Harrell was announced as the starter.
Norris will start on Wednesday if he isn't traded. He'd only have to make a short walk to the home clubhouse at Camden Yards if he's dealt to the Orioles.
Norris is 34-46 in five major league seasons. He's never won more than nine games.
The Orioles also remain in the hunt for Vargas, 30, according to an industry source. The Angels left-hander is "still a possibility" to be acquired before 4 p.m. on Wednesday.
Vargas is 6-4 with a 3.65 ERA in 14 starts this season, and 48-54 with a 4.28 ERA in eight major league seasons with four teams.
Vargas is making $8.5 million this season after his third year of arbitration eligibility. He can become a free agent this winter.
Meanwhile, the Orioles were being shut out with two outs in the fourth, but J.J. Hardy grounded a two-run single into center field to reduce Houston's lead to 3-2.
Harrell walked Manny Machado, Chris Davis and Matt Wieters to load the bases before Hardy singled for his 59th and 60th RBIs of the season - and the Orioles' first hit of the night. Harrell has walked four tonight, raising is American League-leading total to 66.
Davis struck out in his first at-bat, extending his streak to 23 games. He's fanned 40 times during that stretch.
Update: Davis hit his first home run in the second half, a two-run shot to left field in the sixth that gave the Orioles a 4-3 lead and drove Harrell from the game.
Davis hadn't homered since July 14, a span of 11 games.
Harrell walked Nick Markakis to open the inning, his fifth free pass of the night. Adam Jones lined out and Davis belted his 38th homer. He also increased his RBI total to 99.
Chen has a season-high eight strikeouts in six innings. He's retired 11 of the last 12 batters.