Los Angeles has also offered a contract to reliever Dennys Reyes, ESPN reported on Wednesday. In addition, the Dodgers have shown interest in Guillermo Mota, who played for the club from 2002 to mid-2004, and Juan Cruz.
On Tuesday, Thurman said in a telephone interview that the Dodgers and Brewers were the leaders in the race to sign Hoffman.
"We're talking parameters of a deal with both teams," he said. "In the next 24-to-48 hours, I think we'll have something done. If we don't have a deal done, we'll have a pretty solid idea of where he's going. But I think we'll have a deal done."
Hoffman has been on the market since early November, when the Padres took a one-year deal worth $4 million guaranteed with an option for the same money off the table, effectively ending his 16-year tenure in San Diego. The deals being discussed for Hoffman now with the two teams that made the playoffs this past season are worth more than that, but would be at a similar length.
For Hoffman, who is from Anaheim and now lives in North County San Diego, signing with the Dodgers would keep him close to home. But in Los Angeles, hard-throwing right-hander Jonathan Broxton was the closer at the end of the season. He replaced the injured Takashi Saito, who has since been non-tendered, and had 14 saves.
Hoffman, 41, is intent on reaching the 600-save plateau and won't sign anywhere if he doesn't have the chance to be the closer. In Milwaukee he'd have that option after the retirement of Solomon Torres and the departure of free agent Eric Gagne, who left after one shaky year in the Brewers' pen.
To that end, when new Brewers manager Ken Macha learned that general manager Doug Melvin was talking recently with Hoffman's agent, he asked Melvin for permission to call Hoffman himself. Hoffman was vacationing with his family in Hawaii, but returned that call on Saturday.
"I gave him a compliment on his career, and his professionalism," Macha said Tuesday. "A guy with Hoffman's experience and track record, what he's done over the years, would bring a lot of confidence to your team," Macha said. "This guy is a tremendous individual, and he could have a great influence on the young guys on our staff."
Other than free agent pick-up Jorge Julio, who has not been a full-time closer since the first half of 2007, the Brewers currently have no experienced in-house options.
"Yeah, Hoffy's talked to them," Thurman said. "We're talking parameters with them right now."
The Brewers had gotten the feeling all winter that Hoffman, a Californian who had pitched for the Padres since he was traded to San Diego by the Marlins in 1993, was cool on the idea of moving to the middle of the country. But that stance either was overstated or has thawed.
The Brewers also want to add a pitcher to their starting rotation, but Macha, for his part, believes the priority is a top-notch closer. The team showed some interest in left-hander Brian Fuentes and right-hander Kerry Wood before those pitchers signed with the Angels and Indians respectively, and now has focused on Hoffman -- who is coming off a season in which he converted 30 of 34 save chances for a Padres team that lost 99 games and finished last in the National League West.
That the sides are talking marked an improvement. As recently as Dec. 31, Melvin told MLB.com that Hoffman and his agent "haven't given us [the] indication" that they would consider Milwaukee as a destination. That seems to have changed.
"When we talked, he gave his analysis of the Brewers," Macha said. "He said, 'Great offense, a lot of young players and a chance to compete again for a division crown.' Things like that are attractive to him. I can't be the judge of whether the scale is tilted toward pitching in California or just winning, period. I can't give you the complete reading on that. But it is appealing to him that we are a good, young team and we are going to compete."