5:58pm: A National League source told Buster Olney of ESPN.com (on Twitter) that the Mets didn't make an offer to Valverde either.
4:31pm: WFAN's Sweeny Murti tweets that Yankees GM Brian Cashman denied the claims made by Valverde. Cashman said that not only did the Yankees not make an offer, they didn't even have discussions with Valverde and Boras.
3:55pm: Jose Valverde is back in a familiar role as the Tigers' closer, but he could've been in a very different situation had wanted to this offseason. The 35-year-old told Jon Paul Morosi of FOX Sports today that the Yankees and Mets both offered him a Major League contract this offseason (Twitter link).
Neither the Mets or Yankees wound up adding much in the way of bullpen help on Major League deals. The Mets reportedly had interest in Brian Wilson at various points throughout the winter. Ultimately, they elected to sign Brandon Lyon and add Scott Atchison and LaTroy Hawkins on minor league commitments. The Yankees, meanwhile, re-signed Mariano Rivera and swung a deal with the Mariners to land right-hander Shawn Kelley.
Valverde signed a minor league contract with the Tigers in early April which was re-worked into a Major League deal yesterday. The Scott Boras client clearly would not have been a candidate to close for the Yankees with Rivera in the fold, though it seems possible that he could've gotten some save opportunities for the Mets.