Despite the Mets’ lucrative offer to free agent reliever Billy Wagner — supposedly the only one he’s received so far, the NY Times’ Ben Shipgel predicts that as many as 3 other clubs will have something to say about this.

The Phillies, because they rid themselves of $24 million on Thome’s contract, are in position to improve their initial $30 million offer, and there are two other teams expected to make a play for Wagner.

The Boston Red Sox, who have added the front-line starter Josh Beckett and the potential set-up man Guillermo Mota this week in a trade with Florida, would love to add Wagner, according to a person with knowledge of the interest who was granted anonymity because he did not want to jeopardize the talks. And the Braves, if they do not re-sign the free-agent shortstop Rafael Furcal, may elect not to pursue re-signing Kyle Farnsworth and use the saved money toward Wagner.