But that decision will be left to Ron Washington, skipper of the American League and the division-rival Rangers.
"I think it's a pretty big honor to start the All-Star Game," said Weaver, who has those numbers despite missing nearly three weeks on the disabled list with a lower back strain. "Just to be a part of it is an honor in itself, but I think that if Washington picks one guy to start the game, it's a pretty big honor. But I don't think you look at it any differently. It's just a great opportunity to be a part of an All-Star Game."
Other candidates to start include Sale (10-2, 2.19 ERA), former Rangers ace C.J. Wilson (9-4, 2.33 ERA), reigning AL Most Valuable Player Justin Verlander (8-5, 2.69 ERA), the Rays' David Price (11-4, 2.92 ERA) and Washington's own Matt Harrison (11-3, 3.16 ERA). Of that group, only Sale is lined up to pitch Sunday, but the White Sox have already decided that his Tuesday night start will be his last of the first half.
Can Washington pick Weaver as his starter again?
"I have an idea on who I want to be as the starting pitcher," Washington said Tuesday, "and I'll let that be known when the time comes."
The Angels have had a pitcher start the Midsummer Classic in back-to-back years, with Ken McBride doing it in 1963 and Dean Chance getting the honor in '64, but it's never been the same guy.
Weaver was chosen to his third straight All-Star Game on Sunday. He was ineligible to pitch in 2010 because he pitched the Sunday before, and he started the 2011 game when the same thing happened to his biggest competition, Verlander.
Weaver pitched a scoreless first inning in that Midsummer Classic in Phoenix, with one walk and one strikeout.
"I was pretty nervous," Weaver admitted. "It was a packed house and you're going up against the best in their league. Obviously it's a little nerve-wracking, but once you throw that first strike, you calm yourself down."
Weaver would prefer to start, just because he can get his normal long-toss in and it's what he's used to, but he hasn't given it much thought.
"If it happens, it happens," said Weaver, whose next start will come Saturday against the Orioles. "If it doesn't, it's just an honor to be a part of the All-Star Game. It'll be fun just to take part in the festivities, and I think the thing I'm most excited about is watching Mark Trumbo hit homers [in the State Farm Home Run Derby on Monday]."