One thing is for certain though, Rizzo, ranked by MLB.com as the No. 29 prospect in all of baseball, won't make his Major League debut in Arizona this weekend.
"Not in the next few days I know that, not here," Sveum said. "But like I said, it's obviously coming soon."
In 66 games with Iowa this season, Rizzo is batting .350 with 59 RBIs and a Pacific Coast League-leading 23 homers.
After the Cubs finish their three-game weekend set with the D-backs, they'll return home Monday to face the Mets.
"I don't know if there's a date on it," Sveum said when asked if the promotion will come during the upcoming homestand. "We just don't have a date yet."