Woodson's agent, Carl Poston, told ESPN's Josina Anderson that, "the Giants have just put their toe in the water again for Charles Woodson."
The Giants had an initial interest in Woodson earlier in free agency. If Woodson's health checks out, the Giants' interest would likely be for the veteran's minimum. The team has signed many of its veterans in free agency to minimum deals.
Woodson left a visit with the Denver Broncos on Wednesday without a deal. The Panthers and Raiders are also interested in the safety, Poston has said.
"Charles Woodson had a good meeting with the Denver Broncos," Poston told Anderson. "I believe they feel his versatile style will help their defense shine more. We remain in discussions with them. Charles is also still talking to Oakland, and a new team entered the mix during his visit to Colorado."
A source said the Giants are not the "new team" Poston mentioned, however.
Woodson, 36, would be an intriguing piece for the Giants. He could potentially play as one of the team's three safeties utilized often by defensive coordinator Perry Fewell. He also would provide the team with another veteran able to play corner, if needed, as well.
Woodson would provide the Giants with the kind of veteran leadership presence at safety that Deon Grant provided when he played the role of the team's third safety. He also could help fill the void left by Kenny Phillips' departure in free agency to Philadelphia.
The Giants have been actively looking to see what's available on the cheap on the free-agent market. They have been interested in free-agent running back Tim Hightower. According to The Washington Post, the Giants are still interested, along with the Redskins, in the running back's services.