The offer was first reported by Newsday.
Bradshaw, speaking on ESPN's "NFL Live" on Wednesday, said he's been talking to "a lot of different teams" but reiterated he would like to remain a Giant.
"The Giants and Dolphins are ahead of the pack right now," Bradshaw said. "Hopefully someone can use my talents out there and see something in what I have been doing on the field."
"I'd rather stay," he added about New York. "I've set my foundation there in New York and I love just the excitement there. The fans are great. The community is great out there. I love New York the most but the price is going to talk."
Bradshaw was excited to see DeAngelo Williams agree to a monster five-year, $43 million deal with the Panthers, which reportedly includes $21 million guaranteed.
Bradshaw might not get that kind of money, but that deal certainly will not hurt his cause. The South Florida Sun-Sentinel reported that Bradshaw's asking price is not within the Dolphins' price range.
"Well, it's a very exciting deal and hopefully it takes the value up for me," he said. "Hopefully somebody out there can use what I do on the field, that is blocking, running the ball, protecting the quarterback. It just all depends on who can use it and who is willing to pay."
According to The (Bergen) Record of New Jersey, the Giants want to restructure Brandon Jacobs' contract, which has a base number of $4.65 million this season.
Jacobs told ESPNNewYork.com in March that he would be open to the idea if it were realistic.
"If they happen to ask to take the pay cut and it is an unnecessary amount, then absolutely not," Jacobs said then.
"But other than that, if it is something that can be done, then yes, then whatever is going to get the team going and winning.
"But once you take off an astronomical amount, that is not going to happen," he added. "I'd be open to it as long as it is fair to me."
The Giants lost their first big free agent overnight when defensive tackle Barry Cofield agreed to a six-year deal with the Redskins. Cofield will sign a $36 million contract, which will include $12.5 million guaranteed, according to reports.
But they did add a potential new starting center, coming to an agreement with San Francisco center David Baas, a league source confirmed. The move was first reported by the Sacramento Bee.
Baas was the 49ers' center last year, his first season starting at that position. He previously started at left guard and right guard.
The Giants also tried to modify defensive tackle Rocky Bernard's contract, but were unable to do so, according to ESPN NFL Insider Adam Schefter, and now plan to release him.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.