The game will be held at historic Yankee Stadium, and with a new stadium opening up next door, it will be the last All-Star Game to be played there.
Last year, Webb was an injury replacement on the National League team and did not pitch. In 2006, he tossed a scoreless inning.
"Just to be there is an honor, don't get me wrong," Webb said. "But I really want to pitch in that game. I don't think it will be that big of a deal."
Melvin reiterated Thursday that no decision has been made, but his top priority is Webb's health in the second half. How many pitches Webb throws in his Sunday start may determine his All-Star appearance.
"We'll see how we get there," Melvin said. "Nothing's for sure yet. Obviously, I'd like to see him pitch, too, but you also have to understand that based on one day off and then pitching again, there could be a risk. We'll see."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.