The Titans want to use Cook even more as a receiving threat under new offensive coordinator Dowell Loggains, who took over after Munchak fired Chris Palmer on Nov. 26. Cook had not been happy under Palmer, though he carefully watched what he said about the offense.
Even so, Tennessee lined Cook up in the slot and outside preferring to use Craig Stevens or Taylor Thompson more as blocking tight ends. So if the Titans tag him as a tight end, Cook could argue he deserves the higher paying tag of a wide receiver.
Webster said they always have wanted to keep Cook and nothing has changed. Asked if he thought the Titans could sign Cook to a long-term contract or use the franchise tag, Webster said he thinks Cook will be with the Titans this season.
"He's a big part of our offense so how it gets done we'll just have to see," Webster said.
If the Titans can reach a deal with Cook by Friday, that might allow them to tag Bironas, whose four-year, $12 million deal signed in 2009 is expiring. Bironas could be cheaper without the tag after missing six of his 31 field goal attempts last season.
Munchak said what they can't control is when players are ready to talk and work out a deal.
"Most players when they get this close to free agency want to test the market," Munchak said. "That's why we fought for it. I was a part of two strikes to get free agency available for these guys. So a lot of times guys want to wait it out and see. It doesn't mean they don't want to be here, and it doesn't mean we don't want them."