"We don't agree with their evaluation of the player," Urbon told Foxsports.com. "Frankly, we have other offers on the table that are of greater interest to Jason."
The total value of the Red Sox's offer Bay turned down was roughly the same four-year, $60 million contract he turned down in midsummer, according to a baseball source with knowledge of the negotiations. The difference, the source said, was in how the contract was structured, suggesting there may have been a vesting option in the earlier proposal.
The Red Sox have no intention of offering Bay a five-year deal, the source said. If another team -- perhaps the New York Mets -- elects to do so, the Red Sox assume Bay will leave Boston. "If another club offers him five years, my guess is he'll take it in the next few days,'' the source said.
"We've been talking with [the Red Sox] for 10 months," Urbon told the Boston Globe. "We've got to a point where based on the offers we've received from other clubs, we needed to make it clear where we stand, and they've made it clear where they stand. If they want to re-engage at some point in this process but we're not going to wait. We can't wait. We have to go at the pace of the other clubs. I'm sure the Red Sox will have other avenues that they will pursue or they are pursuing."
The Mets offered Bay a four-year deal for between $60 million and $65 million on Thursday, ESPN's Buster Olney reported, according to sources close to negotiations.
Urbon said Bay is not expected to make a decision this weekend.
The Seattle Mariners also have interest in Bay. Although GM Jack Zduriencik has money to spend, they would seem to be an unlikely candidate to offer Bay a fifth year. The Mariners would also like to retain third baseman Adrian Beltre or sign a front-line starting pitcher, like John Lackey.
The Los Angeles Angels, once considered a contender for Bay, said last week they have more pressing issues, namely starting pitching. But it's conceivable, though unlikely, that they could return to Bay.
The Red Sox are also looking at free-agent left-fielder Matt Holliday. But agent Scott Boras is still trying to get Holliday as grand a score as Mark Teixeira got last winter, so serious negotiating has not begun.
Boras also represents Beltre, whom the Red Sox have targeted to replace Mike Lowell if they trade him, as planned, to Texas, but those negotiations also figure to be protracted.
Meanwhile, the Red Sox, as expected, did not tender a contract to outfielder Brian Anderson, a midsummer acquisition from the White Sox.
They also announced that they had signed pitcher Boof Bonser, acquired earlier in the week from the Twins, to a one-year nonguaranteed contract. To complete the deal, the Red Sox sent right-handed pitcher Chris Province, who pitched out of the bullpen for Double-A Portland last season, to the Twins.
Gordon Edes is ESPNBoston.com's Red Sox reporter. Follow him on Twitter.