The truth is this offseason could bring several interesting signings as a result of a paradigm shift to the way the Dolphins approach free agency. That shift puts many more players on Miami’s list of possible additions. How?

Last week, the club confirmed it has “moderate” interest in the Green Bay Packers’ Charles Woodson.

Woodson will be 37 in October. He was sidelined much of last season with a broken collarbone. Regardless of how much he still might contribute to his next team, it’s doubtful he’ll be as good as he was for his last two teams.

And yet the Dolphins are among the interested teams.

Why? Because the team that once held itself to more rigid standards for adding free agents — had to be younger, had to come at seemingly perfect price, had to have right makeup — is loosening some of those bonds.

No, the Dolphins might not be ready to sign someone such as cornerback Aqib Talib and his awesome talent for making plays but also for causing his coaches headaches. But they are eager to win, to improve, to add playmakers. And sometimes getting those involves stretching some philosophical rules.

Maybe the fact the Dolphins are willing to do more than in the past is a reason one club source last week mentioned his affinity for signing Wes Welker in addition to Mike Wallace.

Welker doesn’t fit the Dolphins’ structure if you’re going by the club’s old logic. He’s going to be 32 in two months. He’s going to cost a lot of money and would play a position where the Dolphins are already seemingly set with Davone Bess.

But, the source said, if Welker cannot return to New England with a good contract, he’d love nothing more than to stick it to the Patriots for not retaining him. And the Dolphins might welcome the chance to help Welker with that goal.

Why not?

He makes plays. A lot of them. He has caught more than 100 passes and gone over 1,000 yards in five of the past six seasons. He also has caught 37 touchdown passes in that span.

That makes Welker good enough to blip on the Dolphins’ radar. He is a possibility now — albeit a distant one — where in the past, the team wouldn’t have gotten past his age.

That’s an important shift. And shifting is something the Dolphins needed to do because the old approach was logical but didn’t produce more wins than losses in any of the past four seasons.

So these Dolphins are rethinking, adjusting, and, yes, aggressively trying to not miss out on Mike Wallace.