Other teams may be entering the picture, perhaps even the San Francisco 49ers, who will have to replace starting center Davis Baas, who has reportedly agreed to terms with the Giants.
The Giants released longtime center Shaun O'Hara on Tuesday.
Re-signing Kreutz is important for the Bears, who may have found themselves with more competition for the 13-year veteran than they expected.
Kreutz has turned down more money to remain with the Bears in the past, and will likely do so again. However, the market may be driving up his value.