Davis entered Saturday tied for sixth in the American League with 18 home runs and tied for eighth with 49 RBIs. Vogt was an All-Star last season for the first time. Valencia entered Saturday with a .325 average, which was tied for fourth in the AL (minimum 200 plate appearances). Dull has stranded 30 inherited runners, which is tied for third in the Majors.
"[Davis'] production numbers are terrific, and we have some other guys that are kind of sneaky candidates as well," Melvin said Saturday. "We'll see."
Melvin has not yet lobbied on behalf of his players with Royals manager Ned Yost, who will manage the AL in the All-Star Game on July 12 at Petco Park in San Diego.
"A lot of times I wait," Melvin said. "I know what they're going through. So I kind of wait for maybe a call and if not then try to get my two cents in somehow."
Melvin also feels starting pitcher Rich Hill (8-3, 2.25 ERA) and outfielder Josh Reddick were on their way to All-Star consideration before landing on the disabled list. Both players are expected to be activated next week.
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Following the announcement of the 2016 All-Stars, be sure to return to MLB.com and cast your 2016 Esurance MLB All-Star Game Final Vote for the final player on each league's All-Star roster. On Tuesday, July 12, watch the 2016 All-Star Game presented by MasterCard live on FOX, and during the game visit MLB.com to submit your choice for the Ted Williams Most Valuable Player Award presented by Chevrolet via the 2016 MLB All-Star Game MVP Vote.
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Austin Laymance is a reporter for MLB.com based in Los Angeles. He covered the A's on Saturday.