The All-Star rosters will be announced at 5:30 p.m. CT on Saturday and televised nationally on FOX.
Norris has a case, though the Astros' first-half struggles and low profile could hurt his candidacy. There is no arguing with his numbers, which present a compelling profile.
The righty has a 3.22 ERA with 76 strikeouts in 18 starts, anchoring a burgeoning Houston rotation that has been mostly impeccable since mid-May.
"I think he's definitely getting All-Star consideration," manager Bo Porter said. "I think he's pitched well enough to be one. That's out of our control. I would definitely give him my vote, because he's been our best pitcher the whole year."
Last week, Angels manager Mike Scioscia called Norris "one of the best we've seen" all season. Then how is Norris' 6-7 record so decidedly underwhelming?
Houston has not hit for Norris often, scoring only three runs a game behind him. Over Norris' last 10 starts, that number has been even worse, as the Astros plated just 23 total runs in those outings.
It has left Norris on the hook for no-decisions and losses even when he has shut a lineup down, like last Friday, when he allowed no earned runs in seven innings but the Angels scored three times after he departed to win, 4-2.
"When you talk about wins and losses, a lot of things are out of your control," he said. "It's more about the quality of the outings. How productive is this guy, is the question. The wins and losses don't speak to that."
His ERA could actually drop to 3.06 if he wins an appeal to MLB about a hit call that he hopes to get changed to an error from the White Sox game June 17.
Norris, who has become a trade magnet but has been pledging his commitment to the Astros, said an All-Star nod would be more than just a personal achievement.
"Being an All-Star would be a big deal for me, but also an honor for this organization, too," he said. "I've made my case on the field, but these guys play the defense and get the hits that help me do that."
Chris Abshire is an associate reporter for MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.