The latest NL All-Star balloting update was released on Wednesday and there are still no Giants position players slated to start.
Brandon Belt is second among NL first basemen, trailing Anthony Rizzo of the Cubs.
Buster Posey is second among NL catchers behind Yadier Molina of the Cardinals.
Brandon Crawford is third among NL shorstops, trailing the Cubs' Addison Russell and the Rockies' Trevor Story.
Joe Panik and Matt Duffy are fourth at second and third base, respectively.
Hunter Pence dropped to 10th among NL outfielders.
Four Cubs teammates -- first baseman Rizzo, third baseman Kris Bryant, outfielder Dexter Fowler and second baseman Ben Zobrist -- are within 150,000 votes of one another for the top overall spot.
The remaining NL leaders include: catcher Yadier Molina of the St. Louis Cardinals (933,300); shortstop Addison Russell of the Cubs (1,170,012); and outfielders Bryce Harper of the Washington Nationals (1,451,270) and Yoenis Cespedes of the New York Mets (1,395,577).
The next NL balloting update will be released on Wednesday, June 22. The voting period will be will be open until Thursday, June 30 at 9:59pm PT.
MLB media services contributed to this report