From Jordan Raanan of the Star-Ledger:
An offer was made to Tuck prior to the opening of the "legal tampering" window on Saturday afternoon, a person with knowledge of the situation confirmed to NJ.com. It is believed to have been made at some point in the past week, but no deal was struck between the two sides.
This tells us two things. One, the Giants want Tuck back and, second, Tuck is going to play a little hardball with the Giants in negotiating a new deal.
It's no secret he wants to stay in New York. Much like his former teammate, Michael Strahan, Tuck has made inroads here as a top sports personality and a philanthropist. Leaving New York now to play for a few extra bucks somewhere else just doesn't make sense for him.