10:13pm: Zobrist’s priority is to play for a winning club, tweets Ken Rosenthal of FOX Sports, leaving the Braves “behind” in the race.

Meanwhile, Mets assistant GM John Ricco acknowledged today that the club has serious interest, as ESPNNewYork.com’s Adam Rubin reports. “We’ve had conversations with his guys,” said Ricco of Zobrist, “and we’ll definitely be meeting with them [at the Winter Meetings].” He added: “It’s pretty obvious we think he’s a fit.”

New York expects a decision to be made in the coming days, though it hasn’t apparently been given any such assurances by Zobrist’s camp. The club is “not sure … which direction [it] would go” if Zobrist heads elsewhere, Ricco said. He notes that the Mets haven’t ruled out Daniel Murphy and acknowledged that the team has “touched base” with “all of the free agents,” including middle infielder Asdrubal Cabrera, who Chris Cotillo of SB Nation reported (Twitter link) could be an option.

7:57pm: More than one team is willing to guarantee four seasons in a contract with free agent super-utilityman Ben Zobrist, according to Jon Heyman of CBSSports.com (via Twitter). The Mets are one such club, per the report, which indicates that there are others as well.

Other teams in the mix include the Mets, Nationals, Giants, and a “mystery team,” Heyman says. Earlier today, Marc Carig of Newsday reported (Twitter links) that six clubs remained involved with Zobrist to some extent.

Zobrist wrapped up his on-site visits with a trip to the Giants’ AT&T Park today, MLBTR’s Tim Dierkes has learned. And the hotly-pursued veteran appears to be lined up for a decision in the coming days, as Carig adds.

But that doesn’t mean he’s done with meetings. Indeed, ESPN.com’s Buster Olney tweeted earlier today that Zobrist would meet with representatives of the Nationals at the Winter Meetings — which are being held in his home town of Nashville. And it stands to reason that he’ll have cause to chat with other organizations as well.