Hall's agent, Terry Bross, told the Milwaukee Journal Sentinel on Monday that it would be best for both sides if the third baseman is traded to a club where he could play regularly.
"If Billy's not going to be an everyday player, it's probably best for him and the team to be traded," Bross told the newspaper. "They could get a pitcher for him that would really help the team. I'm sure there are some teams out there that could use a third baseman or shortstop."
Bross also told the Journal Sentinel that a formal trade request had not been made to Brewers general manager Doug Melvin. And while Hall seems on board with the idea, he told the newspaper Bross would do the talking.
"[Bross] knows how I feel," Hall said.
Hall added before Tuesday's game: "I'm not going to be a distraction for this team and what it wants to do."
Hall, 28, publicly voiced his displeasure last week over the call up of Russell Branyan from Triple-A Nashville. Hall, who bats right-handed and entered Tuesday hitting .162 against righties, was told he would be platooning with Branyan at third because of his struggles.
That did not sit well with Hall.
"Obviously, they're not happy with me hitting off righties. I'm not happy with me hitting off righties," Hall said last Tuesday. "[But] I'm not the only one that's struggling with right-handed pitching -- or pitching in general."
Yost said Hall needs to take advantage of the handful of opportunities he's getting against right-handers before he gets another chance to play every day.
"I understand his frustration," Yost said. "But then again, this is a game of production, and you have to be able to step on that field and get the job done."
Yost reiterated that he doesn't consider the situation with Hall and Branyan to be a strict lefty-righty platoon, and Hall very well might get the chance to start against a right-hander in the foreseeable future. But Yost said it would be "foolish" not to keep playing Branyan during a hot streak.
As for Hall's desire to be traded, Yost said it was out of his hands and didn't expect it to become a distraction for the Brewers, who had won seven of their last eight games going into Tuesday night after a disappointing start to the season.
"It's nothing that I focus on or concern myself with," Yost said. "The one thing I will say is that Billy's been 100 percent professional through this whole ordeal."
Melvin spoke with Bross after Branyan was brought up but said the possibility of a trade never came up.
"I didn't get the impression then [that he wanted a trade]," Melvin told the Journal Sentinel. "I don't look at it like [Hall should be traded]. Billy's still a very helpful player on the club against left-handed pitching. We haven't talked about [a possible trade]."
Is Melvin willing to deal Hall?
"I have to do what's best for the ballclub at this point," Melvin told MLB.com. "Right now, Billy has a role on this club and he plays hard. My interest is the big picture and the ballclub. If there is a way to improve the ballclub and it involves Billy or any other player, I will do that. But if it doesn't help the ballclub, I'm not motivated to do anything.
"It's probably tougher to move guys once they want to go."
Hall, who led the Brewers with 35 homers and 85 RBIs at shortstop in 2006, signed a four-year, $24 million contract the following winter. But now it looks like his time is up.
"Billy's done everything asked of him," Bross told the newspaper. "He does lots of stuff in the community. He's thankful to them for signing him to a multi-year contract, but I think it's probably time for a change of scenery.
"If you were the Brewers, why wouldn't you move him? I would think it would be in both Billy's best interests and the team's best interests."
Hall started against the Arizona Diamondbacks on Tuesday, going 1-for-4 with two strikeouts in Milwaukee's 7-1 win.
Brewers fans didn't react strongly when Hall's name was announced before the game, but the boos intensified after Hall struck out for the second time.
"That's not a problem," Yost said. "That just shows you the passion our fans have."
But Hall did single off righty reliever Max Scherzer in the eighth.
Information from The Associated Press contributed to this report.