The 86th All-Star Game will be played on July 14 in Cincinnati.
Rizzo, who garnered a spot on the NL All-Star team last year when he won the Final Vote competition, has received 489,255 votes, and trails Dodgers first baseman Adrian Gonzalez in fan balloting.
Bryant is second among third basemen to the Cardinals' Matt Carpenter, who has received more than 1 million votes. Bryant, who has played 37 games since he was called up in mid-April, has received 583,583 votes. He hit safely in each of his last nine games at Wrigley Field, and was batting .448 with five home runs and 10 RBIs in that span.
"It never crossed my mind," Bryant said of making the All-Star team. "I didn't even know how it works. I still don't know. It's just cool to see that. My goals are never associated with those types of things. I'll continue to go out there and play as hard as I can, and if I end up getting on the team, then that's just icing on the cake."
A three-time All-Star, Castro (571,574 votes) is second to the Cardinals' Jhonny Peralta (595,741) among NL shortstops.
Outfielders Dexter Fowler and Jorge Soler are ranked 14th and 15th, respectively, among NL outfielders. The Nationals' Bryce Harper leads the field and is the top vote-getter so far in the NL.
Fowler has never been named to an All-Star team, and never been among the top 20 outfielders. He expressed his thanks to fans on Twitter: "Never in my life have I made the All Star Ballot update. Just to see my name on that list today is a blessing! #humbleappreciation"
"The one year I thought I should have made it, Bryce Harper made it," Fowler said. "It's definitely an honor to even be mentioned. We have good Cubs fans."
Miguel Montero is third among NL catchers, trailing the Cardinals' Yadier Molina and the Giants' Buster Posey.
"It's an honor," said Montero, a two-time All-Star when he was with the D-backs. "Last year was a little different, to be honest, because I wasn't selected and I had plans with the family."
Then-Arizona manager Kirk Gibson told Montero that 2014 NL manager Mike Matheny wanted Montero on the squad, but Montero was committed to his family that week.
"I told [Gibson] I didn't want to go and he convinced me to go, and I really am thankful he convinced me, because there are things that later on, you could regret," Montero said. "I don't know if I'll be an All-Star again. I'm happy I went."
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 10:59 p.m. CT. 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.
The fans aren't the only ones who get to vote. So do the players, and Montero was ready to click the names of his teammates on the ballot.
"We're going to get a chance to vote, and for sure all the guys on my team will have my vote," he said. "I'm not even going to look at their numbers."