A baseball source said Monday that it's "quite possible" that the 21-year-old will join the team this week.
Rizzo, 21, who is hitting .365 with 16 home runs and 63 RBIs in 52 games with Tucson, was not in the lineup Monday for a game at home against Tacoma.
Tucson manager Terry Kennedy told the Arizona Daily Star that the left-handed-hitting Rizzo was not in the starting lineup so that he could rest a sore left hand that he injured last week during a series in Las Vegas.
Also Monday, first baseman Brad Hawpe made his first appearance in right field this season for the Padres after making 42 starts at first base this season.
Prior to this season, Hawpe had played nearly all of his seven Major League seasons as an outfielder.
San Diego manager Bud Black was asked before the game about Hawpe moving back to the outfield.
"We've [as an organization] talked about it enough to know that [Rizzo's] playing well," Black said. "He's played well. The timing of it [when he's promoted] is when it makes the most sense for him and for us. How he's playing and how we're playing."
Rizzo was one of four players the Padres acquired from the Red Sox in December in the deal that sent first baseman Adrian Gonzalez to Boston.
The thinking at the time -- especially because Rizzo hadn't played a game at the Triple-A level before this season -- was that the first baseman's ETA in the Major Leagues was probably 2012.
But Rizzo started the season swinging a hot bat, hitting .400 in April with seven home runs and 30 RBIs and a .474 on-base percentage. He cooled somewhat in May, hitting .344 with eight home runs and 30 RBIs.
San Diego general manager Jed Hoyer was asked Monday about the speculation that Rizzo's jump to the Major Leagues may be imminent.
"No decisions have been made yet," Hoyer said. "We do believe he's close to ready. We're happy with the progress that he's made. Some of the things we've asked him to do, he's done well."
Hawpe entered Monday's game against the Rockies hitting .243 with four home runs and 18 RBIs. But since April 25, he's hitting .305 with all four home runs and 16 of his 18 RBIs.
As for heading back to the outfield, Hawpe wasn't sweating it.
"The last nine years I've played all right field, minus nine games over the last nine years, so it will be good to get back out there," Hawpe said. "I'm not saying I'm not going to make some mistakes here and there. That's part of the game. I'm human."