PHOENIX -- It used to be the Dolphins really couldn’t compete in free agency when the prize was a veteran who wanted an opportunity to win right away. Places such as New England or Baltimore or Green Bay led the list of destination teams those older decorated players wanted to join to chase a championship.

Well, the Dolphins still aren’t fully in that company. But they’re closer than they’ve been in years.

The recent additions of Mike Wallace as well as other free agents, and the growing belief that perhaps Miami finally has a good quarterback on the roster, has made the team a viable option for players who would have skipped the chance in the past.

And that’s the reason the possibility of adding a gifted veteran such as Osi Umenyiora or Elvis Dumervil is real this offseason. Indeed, the club has spent considerable time studying Umenyiora and even called his representatives to explore the possibility.

He’s on the radar and blinking as much as any 31-year-old player with 26.5 sacks in the past three seasons can in a depressed veteran defensive end market.

The idea of getting Dumervil, a graduate of Miami Jackson, is not quite so far along. The Dolphins think he could be a fit, but there have been no calls and the former Denver Broncos player is not a front-burner issue at the moment.

But down the road, if Dumervil is still on the market, if his price tag is reasonable, and the need to help the pass-rush persists, then the Miami native might be a fit, the Dolphins believe.

The same is not true of free agent defensive end John Abraham. The Dolphins have simply determined he’s not a fit in Miami. Reports he visited the Dolphins were incorrect.

Defensive end is not the only position where the Dolphins believe a veteran might help the team. The club wants to add a defensive tackle because Tony McDaniel, an unrestricted free agent, will not return after four years in Miami.

So that position will be addressed — either with a veteran or a draft pick.

Perhaps safety might also be a place to add experience. The Dolphins did, after all, have what was termed as “moderate” interest in Charles Woodson.

General manager Jeff Ireland used to worry such older players were “progress stoppers” and difficult to fit on a roster he was trying to renew. But the Dolphins are very young now — with fewer 30-year-old players than any time in the past decade — and they can use some experience here and there.

So a veteran coming in and stopping a younger player’s progress is still a consideration, but now Ireland is also weighing how much that veteran can help a young player improve and learn and help in future years — even as the veteran is helping Miami’s cause now.

That shows there is, apparently, more room for nuance now.

The Dolphins, by the way, have not one but possibly two young pass rushers on the roster they believe could use some seasoning. They have two second-year players who could benefit from having a mentor on the team.

Olivier Vernon is one of those. He played a good deal in pass-rush situations throughout the season and even got significant every-down playing time late in the 2012 season. But he still needs work.

The club is also pleasantly surprised and excited about what Josh Kaddu might be able to do as a pass-rusher. Although Kaddu was a rookie linebacker last season and played in only four games, almost exclusively on special teams, he was apparently very active as a pass-rusher in practice.