After MLB Network's Jon Heyman confirmed a report by the Pittsburgh Tribune Review, that according to an unnamed source, Burnett was "open to pitching for a club other than the Pirates," Huntington conceded the possibility the veteran pitcher has hit the open market.
"I can't say he has not. I'm not aware of every discussion there might have been," Huntington said. "All I can say is, he has been very public with his intent to pitch in Pittsburgh or not pitch at all.
"Do I blindly put faith in that? No. But he's been very open with us and continues to be very open."
When reached earlier in the day and asked about any possible updates on Burnett, Pirates manager Clint Hurdle did slightly hesitate before deferring to his GM.
"Neal's finger is on the pulse of this," Hurdle had said.
All along, Burnett was expected to make a final decision on his 2014 fate soon after Masahiro Tanaka entered into a Major League contract, removing the bottleneck from the flow of free-agent starters. That was a prerequisite for Burnett getting a true sense of his open-market value.
Days after Tanaka signed with the Yankees, Matt Garza inked a four-year deal with the Brewers with an annual value of $12.5 million.
In most rankings of all free agents, Garza was followed by Ervin Santana, Ubaldo Jimenez and then Burnett.
Burnett, who turned 37 earlier this month, earned $16.5 million last season while going 10-11 with an ERA of 3.30 and 209 strikeouts in 191 innings.
With the Yankees covering $8.5 million of that, however, only $8 was the responsibility of the Pirates, who did not make the qualifying offer of $14.1 million to Burnett.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.