"Disappointing, but understood," Moeller said after meeting in manager Ned Yost's office. "They've given me a lot of opportunities here, and I respect [the] management a great deal. They gave me an unbelievable opportunity, and, hopefully, I'll be back."
Should Moeller clear waivers, he said he would accept an assignment to Triple-A Nashville.
"I don't know why in the world I would go elsewhere," Moeller said. "I have too many people who like me here, and I like the organization. I just didn't hit. Plain and simple. There isn't any other reason."
Rivera was hitting .298 for Nashville with 10 home runs and 46 RBIs in 58 games. He has not appeared in the Majors since 2003, when he played 19 games for San Diego, and will wear uniform No. 11 for Milwaukee.
"It's tough," said Yost, who had been considering the move for at least a week. "I think it's going to be really good for [Moeller] to get some consistent playing time. He hasn't played consistently in the last two years, and you get a little rusty when that happens."
Moeller played in just 78 games for Arizona in 2003, his final season there, but batted .268 with seven homers and 29 RBIs. He has no doubt that his offensive skills are still there.
"I always hit until I came here," he said. "It's just going down there and rebuilding some confidence and getting some consistent [at-bats]."
Villanueva started against the Reds on Wednesday and pitched relatively well, but because of next week's All-Star break, he was not scheduled to pitch for 13 days. The team decided to pull up Eveland, who will be added to the bullpen mix.
"It's another left-handed arm we can put in the bullpen," Yost said. "Common sense says, 'Get another lefty.' We've just been pounding [Brian] Shouse to death out there. He's done a great job, but you can't continue to use him every single day."
Eveland struggled in an earlier stint with the Brewers, going 0-3 with an 8.51 ERA in five starts. But he is 3-3 with a 1.78 ERA in 11 starts for Nashville.