One of those offers is the four-year, roughly $65 million deal the Mets handed Bay on the final day of theWinterMeetings this week. However, according to various reports, a mystery team - not the Mets - has offered Bay a five-year deal. Possibilities for that mystery team include the Mariners, Giants and Angels.

The Red Sox's reported offer had been four years at $60 million, with a steadfast refusal to add a fifth year because of the club's philosophy against doing so with position players in their 30s.

It was not immediately known if Boston - which is also interested in freeagent left fielder Matt Holliday - had increased the money figure in its most recent offer to Bay.

The announcement from Bay's camp also could be just a negotiating ploy to bring the Red Sox back to the table or get the Mets to increase both the length and value of their heavily backloaded proposal.

But if the mystery team with the fiveyear offer is legitimate, just how serious the Mets are in landing Bay will be known quickly.

The Mets are hesitant to add a guaranteed fifth year for a player of Bay's age, but might have to do so in order to show their disgruntled fan base that the original offer wasn't just a public relations ploy. ESPN.com reported yesterday that the Mets are also thought to have made an offer to John Lackey, the top starter in this year's free-agent class, but a club source denied any proposal was tendered to the Angels righthander.

If the Mets lose out on Bay, they are expected to turn their attention to Lackey to bolster the rotation. At the same time, the Mets likely would look to the trade and non-tendered markets to fill the hole in left field because they have deemed Matt Holliday - the premier left fielder in free agency -too expensive and not a good fit for Citi Field.

*** The Mets declined to tender contract offers to four of their arbitrationeligible players at the leaguewide deadline yesterday: pitchers Tim Redding and Lance Broadway, and outfielders Jeremy Reed and Cory Sullivan. Receiving contract offers from the Mets were right-hander John Maine, relievers Pedro Feliciano and Sean Green, right fielder Jeff Francoeur and backup outfielder Angel Pagan.

Feliciano and possibly Francoeur are thought to be in line for contract extensions this winter that would avoid arbitration.

*** Newly re-signed infielder Alex Cora, who is playing winter ball in Puerto Rico, reportedly left last Thursday's game with a back injury while playing for Criollos de Caguas. The Mets did not have an update yesterday on the seriousness of the injury.