MLB Network's Jon Heyman first reported strong interest in the trio, and MLB.com has confirmed it. The Marlins are willing to spend what it takes to reel in one of the top overall free agents on the market.
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The Marlins, who expect to be active at the Winter Meetings, would prefer to address their pitching needs through free agency rather than trades. They also understand the cost to acquire a closer like Chapman could be a deal in the range of four years and $80 million.
Jonathan Papelbon set the record for the highest salary for a closer in 2012 when he signed with the Phillies for four years and $50 million.
The Marlins on Thursday announced the signing of right-hander Edinson Volquez to a two-year, $22 million contract to help solidify the rotation.
MLB.com and MLB Network will have wall-to-wall coverage of the 2016 Winter Meetings from the Gaylord National Resort & Convention Center outside Washington, D.C. Fans can watch live streaming of all news conferences and manager availability on MLB.com, including the Rule 5 Draft on Thursday at 9 a.m. ET.
Chapman, 28, combined for 36 saves in 2016 with the Yankees and Cubs. Born in Cuba, he would be a natural attraction in Miami, with its strong Cuban-American population.
The left-hander comes off a World Series championship with the Cubs. Throughout the postseason, Chapman had "JF 16" on his cap in tribute to Jose Fernandez, who died in a boating accident on Sept. 25.
The Marlins are also open to signing Jansen, who saved 47 games for the Dodgers this season. The 29-year-old right-hander previously pitched for Marlins manager Don Mattingly in Los Angeles.
A potential drawback to signing Jansen is he declined a qualifying offer. If the Marlins sign Jansen, they would have to part with their first-round Draft pick, which is 14th overall, in 2017.
Melancon, 31, combined for 47 saves between the Pirates and Nationals. The right-hander has previous ties to Jim Benedict, the Marlins' vice president of pitching development. The two were previously together in Pittsburgh.
The Marlins already have an All-Star closer in A.J. Ramos. If the club is successful in adding a top free-agent closer, Ramos would either move to the eighth inning or perhaps be a potential trade piece.