Phillips, who is seeking his first All-Star Game start, is batting .271 entering Tuesday night's contest, with six homers and 31 RBIs. Uggla is batting .264 with 11 home runs and 41 RBIs this year. The leading vote-getter at each infield position and catcher will start in the Midsummer Classic.
But the two-time All-Star said he is focused more on team accomplishments than personal ones.
"I'm worried about the Reds more than anything," Phillips said. "We want to go out there and win as many games as possible."
In the outfield, Reds right fielder Jay Bruce has slipped from ninth place in the voting to 14th, earning 655,098 votes.
Bruce was jumped by the Phillies' Shane Victorino, the Rockies' Carlos Gonzalez, the Pirates' Andrew McCutchen, the Giants' Angel Pagan and the Braves' Jason Heyward.
Bruce, who has 655,098 votes, is batting .265 with 13 homers and 37 RBIs this season.
The top three vote-getters in the outfield are the Dodgers' Matt Kemp (2,589,464), the Cardinals' Carlos Beltran (1,782,831) and the Brewers' Ryan Braun (1,553,356).
Cincinnati's Joey Votto still tops all first basemen, with a resounding 1,257,352-vote lead over the Cardinals' Lance Berkman, who sits in second place. Votto has amassed 2,108,725 total votes, second only to Kemp among all National Leaguers.
"I think it will mean something when the votes are finally tallied up," Votto said. "The last thing I want to do is get ahead of myself, but I am very appreciative of the fans thus far."
Votto, currently batting .355 with 10 homers and 38 RBIs, has appeared in the last two All-Star Games but never started. His 26 doubles, 48 walks and .476 on-base percentage this season are best in the NL.
Cincinnati has not had a starter voted into the All-Star Game since Ken Griffey Jr. in 2007. Scott Rolen, a late injury replacement, started in the 2011 Midsummer Classic in Arizona.
The Rockies' Troy Tulowitzki currently leads at shortstop, the Mets' David Wright has control of third base and the Giants' Buster Posey sits atop the catchers.
Fans can vote for starters up to 25 times at MLB.com and at all 30 club sites -- online or via a mobile device -- using the 2012 All-Star Game MLB.com Ballot until June 28 at 11:59 p.m. ET.
Fans can also once again participate in the State Farm Home Run Derby Fan Poll. Winners will have the opportunity to select three players in each league who they would most like to see participate in the State Farm Home Run Derby. The 2012 State Farm Home Run Derby -- part of Gatorade All-Star Workout Day -- will be broadcast live on ESPN, ESPN HD, ESPN Deportes and ESPN Radio in the United States beginning at 8 p.m. ET on July 9.
The 2012 American League and National League All-Star teams will be unveiled July 1 on the 2012 MLB All-Star Game Selection Show, televised nationally on TBS. Baseball fans around the world will then be able to select the final player on each team via the 2012 All-Star Game Final Vote on MLB.com.
The final phase of All-Star Game voting will again have fans participating in the official voting for the Ted Williams All-Star Game Most Valuable Player Award presented by Chevrolet. During the Midsummer Classic, fans will vote exclusively online at MLB.com via the 2012 All-Star Game MLB.com MVP Vote, and their voice will represent 20 percent of the official vote determining the recipient of the Arch Ward Trophy.
The 2012 All-Star Game will be played at Kauffman Stadium on July 10. Come to MLB.com for extensive online coverage of the All-Star Week festivities.
The 83rd All-Star Game will be televised nationally by FOX Sports, 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 Sirius XM also will also provide comprehensive All-Star Week coverage. For more information, please visit allstargame.com or royals.com/asg.