"I will see what the market is for me," Tuck told the New York Post's Bart Hubbuch on Thursday. "I've never been in this situation before, and it's a great opportunity for myself. I would be doing myself a disservice if I didn't see what the market is, and I will."
After the end of the season, Tuck said he would "love to retire as a Giant" and sounded hopeful a contract would be agreed to during the offseason.
Now Tuck doesn't believe a deal will come to fruition prior to him hitting the free-agent market. He told the New York Post that he plans to sit with the Giants' brass but doesn't believe a contract will come out of the process.
The Giants have salary-cap constrictions and Tuck understands he might command more money on the open market than Big Blue can afford.
"We will sit down in a couple of weeks and see what happens, but obviously, the Giants are going to do what's best for the Giants, and vice versa with me and my family," Tuck added. "I understand where they're coming from and what obstacles they have to overcome this offseason. There's no guarantee, and that's obvious. It's a business, and (I) understand both sides of it."
The nine-year pro has spent his entire career in New York and compiled 11 sacks in 2013. Several veteran free-agent defensive ends -- including John Abraham, Michael Bennett and Cliff Avril -- had trouble getting long-term contracts last offseason. Tuck doesn't sound worried about the market for his skills drying up.
"I'm a pretty good football player," Tuck said, "and I'm pretty sure there will be some interest in a pretty good football player."