The Giants would have received a second-round pick for Cofield during last month's NFL draft, but he couldn't agree on a new contract with the Saints. After that, the Giants told Cofield that he isn't being shopped and won't be traded, the source said.
Cofield, a fourth-round draft pick by the Giants in 2006, is a restricted free agent who hasn't signed his tender. He has started at least 15 games in each of his four NFL seasons, and he has 156 tackles and 6.5 sacks in his career.
The Giants lost their other starting defensive tackle, Fred Robbins, to the St. Louis Rams earlier this offseason. The Giants also have Jay Alford, Chris Canty and Rocky Bernard as experienced players at the position.