"All of these agents think there is more out there," a team official was quoted as saying in the report, alluding to the fact that K-Rod is seeking a longer contract. "They're going to be in for a shock."
The Mets plan on meeting with free-agent closers Brian Fuentes and Trevor Hoffman on Monday.
Rodriguez, 26, saved a Major League-record 62 games last season, and is the top closer available on the free-agent market. Because the Mets are the only Major League team whose top offseason priority is a closer, they are one of the select few reportedly pursuing Rodriguez, who would command more money and likely a longer contract than Fuentes, Hoffman or Kerry Wood.
Minaya said earlier on Sunday that he hoped to leave the Winter Meetings at week's end with new players on his roster.
"In the next four days, we will probably be more aggressive with dialogue with agents," Minaya said. "And at the same time, we have some potential trades that are out there that we might be able to get done."
The Mets are also reportedly interested in J.J. Putz of the Mariners, Jose Valverde of the Astros and Bobby Jenks of the White Sox, three closers who could be available in a trade. And the Newark Star-Ledger reported Monday that the Mets have spoken with the Blue Jays regarding closer B.J. Ryan, though with so many closers available via free agency, it's unlikely that the Mets would part with top prospect Fernando Martinez in a deal.
"It's an area that we're trying to address," Minaya said of his closing situation. "We've been talking to different agents and we've been talking to different clubs, and I feel that this week there's been a lot more dialogue going on than there has been in the past."
Anthony DiComo is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.