General manager Doug Melvin indicated he was still shopping around.
"There may be a couple of pitchers that we're adding to the bullpen here that are still out there on the market," Melvin told the MLB Network Radio channel on SiriusXM. "But we're not going to enter into the high-priced free agents this year. We're going to keep our flexibility."
Pressed by co-host Jim Bowden, Melvin named two free-agent relievers of interest: right-hander Jason Frasor and left-hander Mike Gonzalez, then named three more -- Jon Rauch, Kyle Farnsworth and Ramon Ramirez -- among the "relievers who are still out there and are going to sign. It's just a matter of when."
Frasor, 35, grew up in Chicago and has pitched nine of his 10 Major League seasons with the Blue Jays in the tough American League East. He had a 4.12 ERA in 50 appearances in 2012 and struck out a career-best 10.6 batters per nine innings.
Gonzalez, 34, posted a 3.03 ERA in 47 appearances with the Nationals last season and was of interest to the Brewers before, at the 2009 Winter Meetings before he signed a multiyear deal with the Orioles. He limited left-handed batters to a .179 average last season and would fill a glaring hole for the Brewers, who have no left-handed relief since opting to nontender Manny Parra.
Rauch, 34, had a 3.59 ERA in 73 appearances for the Mets in 2012 and has appeared in at least 50 games in each of the last four seasons. Farnsworth, 36, pitched the past two seasons with the Rays and had a 4.00 ERA in 34 games last season. Ramirez, 31, made 58 appearances for the Mets last season with a 4.24 ERA and has a 3.32 ERA in 417 Major League appearances.
Melvin said he did not have any current negotiations with those players.
He reiterated that the Brewers were counting on John Axford to bounce back from his up-and-down 2012 season to be the closer again and said the team was comfortable with journeyman Jim Henderson in a setup role.
One of the openings could be filled by 6-foot-9, 24-year-old right-hander Johnny Hellweg, one of three prospects acquired in the July trade with the Angels for Zack Greinke. Hellweg has not pitched above the Double-A level, but Melvin said he would get a look in Spring Training.
"Whether he's ready or not, we find out," Melvin said.
Another of the players acquired for Greinke was 22-year-old shortstop Jean Segura, for whom the Brewers have been seeking an experienced backup. Murphy, who signed Monday, could be one candidate.
Murphy's deal included an invitation to the Brewers' Major League Spring Training camp.
The 29-year-old spent the last three years with the Marlins and is a .205 hitter over parts of seven Major League seasons, never appearing in more than 52 big league games in a season. He set that career high last year in Miami, where Murphy made 26 starts -- 17 at third base, eight at second base and one at shortstop.
He has appeared in more Major League games at shortstop (70) than any other position, making Murphy a candidate to back up 22-year-old Brewers starter Jean Segura. The other in-house candidate is Jeff Bianchi, who made his Major League debut for the Brewers last season over 33 games.
In the Minors, Murphy has played 345 games at second base, 255 at shortstop, 22 at third base and one in the outfield. He is a right-handed hitter.
Murphy is the seventh non-roster player added to the Brewers' big league Spring Training camp. The others are right-handers Jairo Asencio and Darren Byrd, left-hander Travis Webb, catcher Blake Lalli and infielder Hector Gomez.