Joseph will certainly draw some interest on the open market next month, should he get there. The Giants will likely make a pre-free agency offer to his agent to see how far apart the two parties are.
Of the top ten free agent defensive tackles on the market, Joseph is the youngest at 25. Many believe he will be lured away regardless of his wishes to stay a Giant.
The Giants are in a financial pickle right now, even after they make the hard cuts they plan on making. The consensus is that Joseph will command around $6 million per year. The Giants may not be able to fit him in.
From Conor Orr of the Star-Ledger:
While the Giants could be in line for some premiere pass rushers in the draft, Joseph's versatility against the run and pass is difficult to ignore. His gap control and ability to create pressure from the interior is among the best in football.
Without him, the Giants would be left with an aging Cullen Jenkins, second-year defensive tackle Johnathan Hankins and Markus Kuhn.