Other than saying that the offer didn't include a guaranteed fifth season, Wren didn't provide any other information about the terms.
A Major League source, who spoke to Burnett on Wednesday night, said the offer was a guaranteed four-year contract with an option for a fifth season. This same source said the option is "very attainable."
"We're not going to comment on offers," Burnett's agent Darek Braunecker said early Thursday afternoon. "I don't feel it's beneficial."
While terms of the offer haven't been revealed, it's believed the Braves have been proposing to provide Burnett with an average annual salary of approximately $16 million.
Last week, Braunecker said that a guaranteed fifth season wouldn't necessarily be a "make-or-break component" of any offer. But at the same time, he said he didn't foresee his client accepting any four-year offers unless they included an average annual salary that was markedly higher than the five-year offers they are seeking.
"What I will reiterate is that if A.J. wants a five-year deal, it's available to him," said Braunecker, while once again not revealing which team would provide this guaranteed five-year offer.
In their search to find an ace, the Braves have been focusing on Burnett for nearly three weeks. On Thursday, they finalized the trade that makes Javier Vazquez the newest member of their rotation.
Braunecker said that the acquisition of Vazquez certainly made the Braves even more attractive to Burnett.
"To me, their situation certainly becomes more appealing to any free agent who is looking to win," Braunecker said. "I think the Atlanta Braves made themselves better by adding Javier Vazquez. I know A.J. would echo that sentiment."
Wren wasn't sure when he might receive a response from Burnett. As for Braunecker, he indicated that he and Burnett are still evaluating a number of different options.
Braunecker said approximately six teams are still showing interest in Burnett. In addition, he indicated that doesn't necessarily mean that these are the same six teams that were showing interest last week.
The Braves, Yankees, Orioles, Blue Jays and Phillies have all reportedly shown interest in Burnett. While they might have had some initial interest, the Red Sox no longer seem to be a potential suitor for the veteran hurler.
Braunecker said he doesn't foresee Burnett signing before the annual Winter Meetings begin Monday in Las Vegas.
There is reason to believe Burnett will at least wait until CC Sabathia determines where he'll be pitching next year. Teams that lose out in the bidding for Sabathia could certainly choose to increase their interest in Burnett.
"I wouldn't say we're in full-fledged negotiations in an effort to get something done yet," Braunecker said. "But that could certainly change with just one phone call. Things have picked up over the past couple of days."
There are certainly reasons to be concerned about offering a guaranteed fifth season to Burnett, who went 18-10 with a 4.07 ERA while completing a career-high 221 1/3 innings and recording an American League-best 231 strikeouts for the Blue Jays this past season.
Burnett has pitched 200 innings during just three of his 10 Major League seasons, and two of those instances came when he had the ability to enter the free-agent market during the ensuing offseason.
But while going 9-2 with 113 strikeouts and a 2.72 ERA in his final 15 starts -- nine of which came against the Yankees, Red Sox or Rays -- this past season, Burnett proved healthy and dominant enough to give a pitching-needy team like the Braves reason to assume the risk that he can provide five healthy and productive seasons.
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.