Free agent running back Pierre Thomas will have his share of suitors. (NFL Game Rewind)

Free-agent halfback Pierre Thomas will draw his share of suitors. (NFL Game Rewind)

NFL teams over the salary cap see the bridge fast approaching. The New Orleans Saints, forced to shed $20 million to get under the weight limit before the new league year begins Tuesday, are one of them.

And as the organization started to do so this Wednesday, veteran running back Pierre Thomas was the first to be let go.

Thomas didn’t weigh heavily against the cap. But by the time the 30-year-old was released, $1.7 million in cap savings and $830,000 in dead money were all that remained from the three-year, $6.9 million contract he restructured last March.

He was one of eight Saints players left from the Super Bowl XLIV team, a team he proved integral to both before and after his 16-yard touchdown screen gave New Orleans a 13-10 lead five Februaries ago. And he could be one player the New England Patriots find interest in after this February’s team.

New England heads into free agency with dominoes yet to fall went it comes to cornerback Darrelle Revis’ 20 million option, the potential restructure of receiver Danny Amendola’s deal or linebacker Jerod Mayo’s, as well as the looming unrestricted free agency of free safety Devin McCourty.

Defensive tackle and team captain Vince Wilfork announced Thursday that the Patriots will not pick up his two-year option. But there are more dominoes in play as the organization vies to get under the adjusted cap number.

One of them resides in the hands of halfback Shane Vereen, who, along with fellow Patriots rusher Stevan Ridley, are also scheduled to become unrestricted free agents in the coming week.

The availability of Thomas could present New England with an alternative to the 2011 second-round pick out of California more so than the third-round pick out LSU. Yet that alternative, four years older, one inch taller and 10 pounds heavier, is something to consider. It is something of a contingency plan, should Vereen not return to the team that drafted him four years ago, and the one he caught 11 passes for last month.

Thomas draws some semblance in terms of role. But he’s a different kind of player cut out for that role. He isn’t electrifying. He isn’t a mismatch out wide. What he is, is in a sense, indicative of the way he entered the league.

Not invited to the NFL Scouting Combine and not drafted by an NFL team in 2007, the Illinois product made his home in New Orleans by doing the little things. Those little things made him an every-phase player. His impact on special teams, as well as his impact as a pass blocker, a receiver and a rusher, kept him there for eight seasons.

Thomas carved his place, whether it be as a returner during his early years, or as a third-down threat from “11” personnel in his later years. Throughout, he finished plays low to the ground with his legs still churning. And from beginning to end, he finished having played in 105 regular-season games for the Saints, amassing 3,745 rushing yards on 818 carries, 2,608 yards on 327 catches, and 40 total touchdowns.

He rushed for 4.8 yards per carry in five of his campaigns with New Orleans, and 4.9 as recently as 2014. And although it was also in 2014 that Thomas was limited to a career-low 222 rushing yards, catching as many passes – 45 – as carries he had handled, he pieced together a career-high 34.4 receiving yards per game.

One turn back to quarterback Drew Brees at a time, the high-percentage plays added up. The season, though, did not add up to what it could have.

The 5-foot-11, 215-pound back missed five games because of foot and rib injuries. The latter ultimately sent him to injured reserve before Week 17, as he quietly left in the middle of his final game as a member of the Saints.

Quietly, he left the Saints fourth in franchise history in rushing yards, sixth in receptions, and 14th in receiving yards.

There’s reason to believe what he has left should continue to translate not far from the way it already has. When healthy, Thomas has been reliability. He had missed one game over his previous three seasons heading into 2014, but it’s his steadiness out of the backfield, his blitz pickup, his ball security, and what he’s done to provide another layer to a rotation that has kept him going.

Thomas’ greatest runs in a Saints uniform were without finesse or breakaway speed; they were subtle. They were smooth more than they were sudden. His patience to allow the blocks on his slip screens to develop, his agility to shift just enough into space, his vision to run by tackles, his strength and balance to bounce off of them – all of which are still part of his mold.

And should the Patriots’ backfield take on a new shape, his mold could be fit for it.