According to co-owner John Mara, the Giants want to retain Cruz long-term, but "there's a limit" to what they'll pay him.
"If he took our offer, he'd be a very wealthy man," Mara said, adding, "if someone is willing to pay more than we are, then we'll have to say goodbye."
Last week, coach Tom Coughlin told ESPN New York he'd like to see the team keep Cruz.
During the NFL Scouting Combine last month, reports surfaced the Giants would likely place a first-round tender on Cruz, guaranteeing him a one-year salary at about $2.9 million. Cruz would be eligible to receive offers from other clubs, but New York would have the ability to match them or receive the appropriate compensation should he leave.
Dwayne Bowe’s new five-year, $56 million deal, including $26 million in guaranteed dough, is the standard for Cruz.
In addition, the team would like to lock up wide receiver Hakeem Nicks and perhaps re-sign tight end Martellus Bennett.
Other RFAs being tendered were safety Stevie Brown and running back Andre Brown, both of whom received second-round levels.
Follow Sam on Twitter @SamSpiegs