There has been a flurry of activity in the nascent stages of NFL free agency and for the Giants, it has been a case of making calls, expressing interest, talking numbers, but not yet cashing in with any players.

Of course, the official period to sign players outside the organization doesn’t begin until Tuesday, but there has been plenty of negotiating throughout the league the past three days. The Giants made a determined run at defensive end Brandon Graham — and might have thought they had him — but Monday he re-signed with the Eagles and so the search continues to add a pass rusher and a safety capable of starting.

How serious are the Giants about bringing in an elite safety? They were “very active’’ in the Devin McCourty chase, according to a source, but ultimately did not match the Patriots’ mega-deal (five years, $47.5 million with $28.5 million in guaranteed money).

The Eagles, with the 13th pick in the first round of the 2010 NFL Draft took Graham out of Michigan and two picks later, at No. 15, the Giants took Jason Pierre-Paul. Five years later, the Giants were hoping to pair Graham with JPP but Graham re-upped with the Eagles on a four-year, $26 million contract ($14 million guaranteed).

There is no secret the Giants are on the lookout for another pass-rusher and they thought the 26-year old Graham would be a good fit. Jabaal Sheard (Browns) and Derrick Morgan (Titans) are available options. Another interesting player is Adrian Clayborn, a 2011 first-round pick of the Buccaneers who has missed 28 games in his four-year career, but has 13 sacks in the two seasons he was healthy.

Five years and five days ago, the Giants made Antrel Rolle the highest-paid safety in NFL history and general manager Jerry Reese, not balking at the costly addition, described Rolle as “a young, ascending, veteran player.’’

Five years and five days later, the Giants are looking for the same thing all over again: A young, ascending, veteran player, this time very likely to replace Rolle as a starting safety.

That search could lead them to Ron Parker, who in some ways is eerily similar to the 2010 Antrel Rolle.

Both are 6-foot and 206 pounds. Rolle was 27 when he came to the Giants; Parker is 27. The big difference is Rolle was a high first-round draft pick of the Cardinals from a big-time program (Miami).

Parker, undrafted out of largely unknown Newberry College, — the same school that produced Giants receiver Corey Washington — kicked around with the Raiders, Panthers and Seahawks before finally getting on the field with the Chiefs.

Parker in 2014 became a starter for the first time in his four-year career when star safety Eric Berry was forced off the field to deal with lymphoma.

As free agency kicked off Saturday, with teams allowed to open negotiations with agents, the Giants inquired about Parker, one of more than a handful of teams — including the Jets — to express interest.

The Giants also have interest in Rahim Moore, who is 25 years old and certainly fits the “young, ascending, veteran player’’ Reese seems to be looking for. Moore is a far more proven commodity than Parker, having started 48 games the past four years for the Broncos.

The Giants have not closed the door on a return by Rolle, 32, but he will hit the market and is likely to have suitors. He tweeted Monday he’d like to play with “my brothers’’ Andre Johnson and Vince Wilfork — former teammates at the University of Miami. He also posted a statistical comparison of himself, Parker, Moore and McCourty.

“But they still doubt me becuz I am 32,’’ wrote Rolle, who did not miss a game in five years with the Giants.

There’s a good chance the Giants will resign Stevie Brown, but that won’t stop them from looking to add a top-tier starting safety.

The Giants would also like to add a speed/pass-catching running back to complement Rashad Jennings and Andre Williams and have interest in Shane Vereen, who amassed 99 receptions the past two seasons for the Patriots — and caught 11 of Tom Brady’s passes in the Super Bowl victory over the Seahawks. The Giants have some level of intrigue in the big-play potential of Antone Smith of the Falcons — who last season took a screen pass 74 yards for a touchdown against the Giants — and the passing-game production of Washington’s Roy Helu, who has 129 receptions in 48 NFL games. The desire is to find a back with at least some of the skill-sets of retired David Wilson.

LB Jon Beason had to agree to a pay cut to remain on the roster and he has accepted a reworked deal.

The Giants will save about $3.2 million on their salary cap with the savings from Beason.