The opportunity is there for the New Orleans Saints to put together a very strong offseason.

It cost them standout wide receiver Brandin Cooks, which is no small price to pay, but now the Saints are in position to significantly improve a defense that has ranked near the bottom of the NFL each of the past three seasons.

Improvement doesn’t hinge on landing cornerback Malcolm Butler, who will visit this week, coach Sean Payton told The Associated Press on Tuesday. But finding a way to get him in black and gold would drastically change the conversation about this roster. Instead of having some nice additions on defense who could make things better, suddenly this would look like a roster very close to competing for a playoff spot.

That much shouldn’t be put on one player, and the level of hope would depend on the compensation New Orleans surrenders to acquire Butler from New England, but the Saints would be close if this deal comes together. Most of the major holes have been plugged on defense. A.J. Klein takes care of linebacker. Keeping Nick Fairley solves the interior rush. And Alex Okafor, added Tuesday, gives the team someone to rotate into the pass rush.

That leaves cornerback and another edge rusher, which were and remain the biggest areas of need. The market for pass rushers never developed, and the top two cornerbacks — A.J. Bouye and Stephon Gilmore — went elsewhere.

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Getting involved with some of the other cornerbacks would have meant having to pay someone like Logan Ryan, who is a solid No. 2 player, in the range of $10 million per year. While it will cost some draft picks as well as a new contract to acquire Butler, his talent is undeniable, and he’s significantly better than anyone on the free-agent market.

His addition would give the Saints, along with Delvin Breaux, two cornerbacks capable of pressing and playing zone, which would be very appealing to defensive coordinator Dennis Allen. With those two in the fold, the front seven would have more time to get after the quarterback, which has been an issue the past two seasons.

The issue will be acquiring him. Butler is a restricted free agent and was tendered at the first-round level. That means, unless another deal is worked out, New Orleans could sign him to an offer sheet and see if New England matches. If the Patriots decline, Butler would come to New Orleans, and New England would be awarded the Saints' 11th overall draft pick as compensation.

The desired outcome would be for the Saints to agree on the parameters of a long-term deal with Butler and then discuss different compensation with the Patriots, which would likely center on the 32nd overall pick (acquired in the trade for Cooks) or New Orleans’ second- and third-round selections.

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Obviously, paying less to acquire Butler would be better. If the Saints can land the cornerback and hold onto the 11th pick, it would be hard to view this as anything other than a win for the organization.

That would allow New Orleans to add another piece early in the draft. If that player happens to be a pass rusher, all the better. Even if not, if Butler enters the fold, the Saints will have plugged enough holes to have the flexibility to play the board and focus on drafting talented players, regardless of position.

There will still be work to be done, even with Butler. The Saints will need to blend all the pieces together and find a way to get pressure on the quarterback. And, as far as the playoffs are concerned, the NFC South has become a difficult division. Carolina and Atlanta made the past two Super Bowls, and Tampa Bay continues to get better.

The schedule also doesn’t help. New Orleans has to play the NFC North and will have some tough games against the AFC East. But the potential is there.

The Saints have already gotten better. By adding Butler, the stakes would only get higher.

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