Choate, who signed a three-year deal with the Cardinals, and Burnett, who took two years from the Angels, were among a number of lefty relievers under consideration by the Brewers, who have a need since non-tendering Manny Parra last week.
Among the free-agent lefties still available are Mike Gonzalez, Tom Gorzelanny, J.P. Howell, Will Ohman and Hideki Okajima.
General manager Doug Melvin happened to meet with Howell's agent on Wednesday, but would not say which of Greg Genske's players they discussed. Melvin did say that as of Wednesday afternoon, he had yet to make any formal offers to free agents.
The Brewers might pick a player in Thursday's Rule 5 Draft but otherwise return to Milwaukee with no new players to show for his week at the Gaylord Opryland Resort & Convention Center.
"We do get a chance to go through a lot of stuff here with our staff, go through the roster, go through the teams, you filter through a lot of things that you think might happen," Melvin said. "If somebody comes up with an idea -- 'Would they do this? Would they do that' -- we just flat-out make the call and find out."
Melvin is also looking at right-handed relievers but seemed to downplay the Brewers' chances of landing veteran Jason Grilli when he said he hadn't spoke with Grilli's agent, former Brewers shortstop Gary Sheffield, in Nashville. Grilli himself tweeted early Wednesday that he was in town, presumably to meet with teams, but as of Wednesday afternoon, nothing with the Brewers had been scheduled.
Other Day 3 tidbits:
Genske's highest-profile free agent this winter is right-handed starter Edwin Jackson, a player of interest for Milwaukee.
Jackson, 29, was 10-11 with a 4.03 ERA in 31 starts for the Nationals last season while earning $11 million on a one-year deal. He and fellow right-hander Ryan Dempster could be good targets for the Brewers if they are willing to take a two-year deal.
A report that said the Brewers had contacted the Rangers about left-handed starter Derek Holland was false, Melvin said.
The Brewers are not shopping right fielder-turned-first baseman Corey Hart, who is entering the final year of his contract, but would listen to offers from interested teams. Hart has expressed interest in an extension to remain in Milwaukee but the Brewers have yet to engage in serious discussions with agent Jeff Berry.
Melvin's best chance for adding a player might come Thursday morning at the Rule 5 Draft. The Brewers own the 16th selection and have a target in mind, though Melvin would not say whether it was a pitcher or a hitter.
He did not want to tip his hand, worried that other teams were interested in the same player.
"The chances of getting the guy, probably, are slim," Melvin said.
If the Brewers do make a selection in the Major League phase of the Rule 5 Draft, they must keep that player on the active roster all season or offer him back to his original team for half of the $50,000 claim fee.
The chances of the Brewers losing a player on Thursday are greater. As a gesture of goodwill to a longtime farmhand, they only protected Minor League second baseman Eric Farris at the Double-A level, meaning Farris is available to teams in the Triple-A phase of the Rule 5 Draft.
With Milwaukee, Farris is blocked by incumbent second baseman Rickie Weeks, and prospect Scooter Gennett is expected to start 2013 at Triple-A Nashville.
"It's more of a gesture to [Farris]," Melvin said. "We've talked to clubs to try to help him out."
The Brewers did make two Minor League signings on Wednesday, inking right-hander Chris Jakubauskas and infielder Hainley Statia to deals that do not include invitations to Major League Spring Training camp. Statia hit .257 in 108 games for Double-A Huntsville and Triple-A Nashville in 2012, and Jakubauskas had a 4.29 ERA in 27 games (eight starts) for three different D-backs and Blue Jays affiliates.