Melvin said the Brewers were also preparing an initial offer to Sheets. Sabathia, though, is the free agent on most Brewers' fans minds.
"We'll make the offer and go from there," said Melvin, who did not expect a quick response. Teams own exclusive negotiating rights with their own free agents for the 15 days following the World Series, but players almost always wait to test the open market.
That will surely be true of Sabathia, who went 11-2 with a 1.65 ERA in 17 Brewers starts and will be the most sought-after arm on the winter free-agent market. Melvin said he has already had several conversations with Greg Genske, one of Sabathia's representatives.
Other teams can contact Sabathia's representatives during the Brewers' 15-day window, but they are barred from making formal proposals.
"He's not going to be a guy who has 27 phone calls," said Melvin, noting that the market for Sabathia will be limited to the Brewers and a few big-market ballclubs. "He's going to get five. Right? If he's going to demand the money that he's going to demand, he'll get a lot fewer phone calls than Ray Durham or some of the other [free agent] players we have. The realistic phone calls will, I think, be a very small number."
Melvin wanted to make his initial offers before leaving Milwaukee on Saturday for the General Managers Meetings. That apparently will include an offer for Sheets, who has pitched all eight of his Major League seasons for Milwaukee and made four All-Star teams.
"I've talked to Casey Close," Melvin said, referring to Sheets' agent. "I told him we'll keep the door open. I know they want to go through the [free agent] process but I am going to meet with Casey at the GM's Meetings next week."
It is unclear whether the Brewers plan to pursue Gagne, who finished the season strong after a poor start to his lone season in Milwaukee, or Lamb, who joined the team in September. Shouse, who turned 40 in September, has been a key member of the bullpen for the past two seasons and said he prefers to return, but would like a two-year contract.
"My first choice is to go back to Milwaukee, but I also feel that I owe it to myself and to my family to possibly see what else is out there and what could happen," Shouse said on Thursday. "I've always wanted to get a two-year deal somehow, and we'll see if that's a possibility either out there somewhere or with Milwaukee."
He did not have discussions with Melvin during the season, per a team request.
"I guess I have to try to keep my options open," Shouse said.