A source confirmed to ESPNNewYork.com the planned tender for Cruz, which hasn't yet officially been made by the team.
The two sides have been unable to reach an extension so the team will tender the highest RFA tender available, worth $2.879 million for this season, to Cruz.
The first-round tender also means that the Giants will have "the right of first refusal" if another team makes Cruz a lucrative contract offer. The Giants can match any deal made by another team or receive a first-round pick as compensation if they refuse to match.
"Certainly, we're taking a risk, but we would still have to right to match and if we decided not to do that, we're getting a first-round draft pick out of it," Mara told reporters, according to the Star-Ledger. "So yeah, it is a risk for us, and he is an exciting, dynamic player. It's not going to shock me if somebody makes him an offer."
The Giants also tendered safety Stevie Brown and running back Andre Brown at second-round tenders, worth $2.023 million in salary. Mara, speaking to reporters at an NFL event, said the team did not tender restricted free agent running back Ryan Torain, who still could re-sign with the team later.
The Giants want to re-sign Cruz to a long-term deal but the two sides have been apart on financial terms. Cruz's camp will want to see how much wide receivers like the recently traded Percy Harvin, and free agents Greg Jennings and Mike Wallace will sign for soon.
"Certainly we have the wherewithal to match just about any offer," Mara said, according to the Star-Ledger. "It's just a question of whether we want to do it and what the number is going to be. We've made him a very substantial [extension] offer but his agent feels like he wants to test the market a little bit and that's his right to do that. Again, we'd love to have Victor back. He's been a great player."
The Giants are taking a risk by tendering Cruz since their cap space is somewhat limited and they still need to re-sign free agents such as left guard Kevin Boothe and tight end Martellus Bennett. The team also wants to sign Hakeem Nicks to a long-term extension with the wide receiver entering the final year of his deal.
Teams typically do not show much interest in restricted free agents but Cruz, 26, is coming off two incredibly productive seasons with a total of 168 catches for 2,628 yards and 19 touchdowns.
The Giants hope that the RFA tender will allow them to keep Cruz for this season and give them more time to negotiate a long-term extension.
Mara declined to go into detail when asked how far apart the Giants and Cruz are from agreeing to an extension.
"I'm not going to get into dollars," Mara said, according to the Star-Ledger. "I don't want to characterize [the gap]. Let's just say if he took our offer, he'd be a very wealthy young man."