The news was first reported by Newsday.
"We're looking for somebody who can pitch at the back end, somebody who has a demonstrated track record recently and somebody that fits and has known Mickey in some capacity in the past,'' Mets general manager Sandy Alderson said without confirming the deal.
Swarzak, acquired at the trade deadline from the rebuilding Chicago White Sox, bolstered the Milwaukee Brewers' bullpen down the stretch as the they made a push for a National League wild-card spot. He finished 6-4 with a 2.33 ERA and two saves in 70 relief appearances combined with Milwaukee and the White Sox.
The 32-year-old right-hander spent the first five seasons of his major league career with the Minnesota Twins after his second-round selection in the 2004 amateur draft. He also has pitched for the Cleveland Indians and New York Yankees.
New York also is looking to add offense, either from first base, second or the outfield. Alderson is willing to wait.
"Typically toward the end of the offseason there are some players available at perhaps better prices,'' Alderson said. "But that doesn't mean they're better value. Sometimes they are; sometimes they aren't. Certainly knowing those possibilities arise late helps maintain a certain amount of discipline and patience in days like the winter meetings.''