Cozart is in fourth place among shortstops with 431,365 votes. Another Cardinal, Jhonny Peralta, is in first place with 595,741.
Phillips is in fourth place at second base with 337,146 votes behind leader Dee Gordon (934,249) of the Marlins.
Votto rounds out the pack, currently in fifth place at first base with 384,285 votes. Adrian Gonzalez of the Dodgers leads the voting with 929,016.
Cozart is looking for his first All-Star Game appearance, while Frazier was selected to his first career All-Star Game last season. Phillips is a three-time NL All-Star, and Votto is a four-time NL All-Star.
Fans can cast their votes for starters at MLB.com and all 30 club sites -- on their computers, tablets and smartphones -- using the 2015 Esurance MLB All-Star Game Ballot until Thursday, July 2, at 11:59 p.m. ET. For the first time, voting is exclusively online, where fans may submit up to 35 ballots.
Fans may also receive the ballot by texting VOTE to 89269 (USA) or 101010 (Canada). Or text VOTA for a ballot in Spanish. Message and data rates may apply. Up to five messages. No purchase required. Reply STOP to cancel. Reply HELP for info.
Following the announcement of the 2015 All-Stars, be sure to return to MLB.com and cast your 2015 Esurance MLB All-Star Game Final Vote for the final player for each league's All-Star roster. On Tuesday, July 14, watch the 2015 All-Star Game 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 2015 MLB All-Star Game MVP Vote.
MLB.com will provide extensive online coverage of All-Star Week festivities.
The 86th All-Star Game will be televised nationally by FOX, in Canada by Rogers Sportsnet and RDS, and worldwide by partners in more than 200 countries via MLB International's independent feed. ESPN Radio and ESPN Radio Deportes will provide national radio coverage of the All-Star Game. MLB Network and SiriusXM will also provide comprehensive All-Star Week coverage. For more information, please visit allstargame.com.