In the past 40 years, they've used a No. 1 choice on a quarterback only twice: Bob Griese in 1967 and Dan Marino in 1983. Both are members of the Pro Football Hall of Fame.
With four selections in the first three rounds, the Dolphins are almost certain to pick a passer today, perhaps even in the opening round with Notre Dame's Brady Quinn. Possibilities in the second or third round include Trent Edwards of Stanford, John Beck of Brigham Young, Matt Moore of Oregon State, Drew Stanton of Michigan State and James Pinkney of East Carolina.
One of them likely will be the first quarterback drafted by Miami since Josh Heupel of Oklahoma in the sixth round in 2001.
"There are five or six guys who are probably first-day worthy," general manager Randy Mueller said. "It's a really good group. I think there will be some guys picked probably even outside the first round who end up being players in this league.
"Everybody has a different flavor they like. That's why Baskin Robbins has 31 flavors. We get to pick the kind we like."
In addition, the Dolphins may be close to completing a long-anticipated deal to acquire 36-year- old Kansas City quarterback Trent Green. He would serve as caretaker at the position while the youngster drafted today is groomed for the job.
Quinn could be taken as high as No. 1 by Oakland. More likely he'll be the second passer picked, following JaMarcus Russell of LSU. The Dolphins have some flexibility with 10 draft selections, including two second-round choices, and they might try to trade up from their No. 9 spot to acquire Quinn.
Miami is the lone team in the AFC East with an unsettled quarterback situation. New coach Cam Cameron acknowledged the position is a big question mark.
"I am sure you are trying to figure it out, and I don't blame you," Cameron said. "I want to figure it out, too - who is going to be the Dolphins' quarterback?"
Such comments suggest it won't be Daunte Culpepper, who is still struggling to fully recover from reconstructive knee surgery nearly 18 months ago.
A three-time Pro Bowl quarterback with the Minnesota Vikings, Culpepper was denied medical clearance to participate in minicamp this month, and there has been increasing speculation this week he'll soon be traded or released.
Culpepper said his knee is improving, and he expects to increase activity next month.
"I am continuing to do everything I can to prepare to play at the level of expectations of the Dolphins (if they keep me), the NFL fans and most importantly myself," Culpepper wrote in an e-mail. "Until this week, it never entered my mind that I wouldn't be the starting quarterback of the Miami Dolphins this coming season."
Former coach Nick Saban used a second-round draft pick a year ago to acquire Culpepper, who arrived touted as a franchise quarterback but played in only four games. It wasn't the first such deal that backfired on Miami: Saban's predecessor, Dave Wannstedt, spent a second-round choice in a 2004 trade to acquire quarterback A.J. Feeley, a washout.
Such trades are a big reason the Dolphins have missed the playoffs the past five years, a franchise record. And they're still seeking an adequate successor for Marino, who retired in 1999.
Cameron, a former quarterback, seems intent on resolving the situation. Joey Harrington, who started 11 games in 2006, was released in March, and Culpepper could be next.
The draft offers a chance to restock. In the past 16 years, the Dolphins have drafted only three quarterbacks: Heupel, John Dutton in 1998 and Mark Barsotti in 1992. None made the regular-season roster.
But Mueller and Cameron want to build through the draft at quarterback and elsewhere. The Dolphins' 10 picks would be their most since 1998, and they have four of the first 71 choices.
"By being able to acquire a few extra picks, we've given ourselves some options," Mueller said.
If Miami fails to acquire Quinn, possible choices in the first round include Penn State left tackle Levi Brown and Ohio State receiver-returner Ted Ginn Jr. The first day of the draft may be devoted entirely to shoring up an offense that averaged 16.3 points per game last year, the Dolphins' lowest figure since 1967, Griese's rookie year.