Ortiz was the starter at DH for the AL the past three seasons.
Big Papi mashed career homer No. 450 in Sunday's 8-5 win against the Yankees, and he has 19 long balls on the season.
When Ortiz hits his next homer, it will mark the 13th consecutive season he's hit 20 or more.
Cruz had 2,944,267 votes when the latest round of balloting was released on Monday, while Ortiz had 1,948,211.
Fans can cast their votes for starters at MLB.com and all 30 club sites -- online or on a mobile device -- using the 2014 All-Star Game MLB.com Ballot Sponsored by Experian until Thursday, July 3, at 11:59 p.m. ET. The 2014 All-Star Game will be played at Target Field on Tuesday, July 15.
Fans may submit up to 25 online ballots, but they can also earn a one-time bonus of 10 additional online ballots. To access these additional online ballots, you must be logged into your MLB.com account when you submit any online ballot. If you do not have an MLB.com account, register on the site in accordance with the enrollment instructions for a free MLB.com account.
Fans this year once again can participate in the Home Run Derby Fan Poll. Fans will have the opportunity to select three players in each league who they would most like to see participate in the Gillette Home Run Derby. The 2014 Home Run Derby will be broadcast live on ESPN, ESPN HD, ESPN Deportes and ESPN Radio in the United States beginning at 8 p.m. on Monday, July 14.
The 2014 AL and National League All-Star teams will be unveiled on the Taco Bell All-Star Selection Show on Sunday, beginning at 7 p.m. on ESPN, with further details to follow on MLB.com. Immediately following the announcement of the AL and NL All-Star rosters, fans can begin voting to select the final player for each league's 34-man roster via the 2014 All-Star Game MLB.com Final Vote Sponsored by Experian. Fans will cast their votes from a list of five players from each league over the balloting period.
And the voting doesn't end there. The final phase of All-Star Game voting will again have fans participating in the 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 2014 All-Star Game MLB.com MVP Vote Sponsored by Pepsi, and their voice will represent 20 percent of the overall vote that determines the recipient of the Arch Ward Trophy.
MLB.com will provide extensive online coverage of the All-Star Week festivities.
The 85th 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.
Manager John Farrell and his entire coaching staff will represent the Red Sox at the All-Star Game as a result of last year's World Series championship.
It remains to be seen which players will join them.