If they do though, they'll have to make a stronger attempt.
According to Ralph Vacchiano of the New York Daily News, Phillips rejected the Giants' offer and will likely test free agency.
The 26-year-old strong safety has been with the team since being picked in the first round of the 2008 NFL draft, but has had his share of injuries.
Phillips missed most of the 2009 due to a severe knee injury and only played in seven games in 2012.
With Phillips out, the Giants got great production from Stevie Brown, who led the team in interceptions, but even with Brown, the secondary still struggled.
According to Vacchiano, Phillips would prefer to remain with the Giants, and the team wants to bring him back, but it looks like their prices aren't matching up.
So for now, it looks like Phillips will be hitting the free agent market in hopes of landing a top deal.
The offer made to Phillips wasn't announced to the press, nor was the contract offer Phillips was hoping to land.
Many Giants fans are hoping that Phillips will return to the team and join a three-safety rotation that includes him, Brown and Antrel Rolle.
But it's looking more and more like the Giants may end up losing Phillips to another team if they don't increase their efforts to keep him.
Stay tuned, Giants fans.
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