Henne, who watched practice for the second day in a row Wednesday, went for a second opinion on his shoulder. The team is trying to decide what direction to take and have ordered those involved not to discuss Henne's injury until they figure out what to do.
Henne's injury, suffered in Miami's Week 4 loss at San Diego, appears to be more extensive than just a first-degree separation, which could be padded up and protected so that he could play. Second- and third-degree separations are more serious, and the wrong hit could make the injury worse and force a surgery.
According to a source, the team should update Henne's situation in the next day or two. The Dolphins are in a bye week so there is no urgency to make an announcement on Henne's status.
Delhomme declined to visit. Contract numbers were discussed with Garrard, according to a source, but those talks went nowhere. Croyle and Edwards left their workout without a contract offer.
Matt Moore replaced Henne in Sunday's game at San Diego and immediately drove the Dolphins to their only touchdown. He finished 17 for 26 for 167 yards and had several passes dropped.
Moore went 1-4 as a starter last season for woeful Carolina. If he gets the call against the New York Jets on "Monday Night Football" on Oct. 17, he would become the 16th starter at quarterback in the 13 seasons since Dan Marino retired.
With Henne out, Moore is taking all of the snaps with the first team in practice.
"It has been good getting in there and getting a lot of much-needed work," he said. "I need the reps, and it's good for everybody to get the reps with me as well. The only way to get on the same page with everybody is to practice with them."
A fourth-year pro with 23 career starts, Moore acquitted himself well coming off the bench in San Diego.
"There were some plays I wanted back," Moore said. "There were some good things I'm happy about. I'm disappointed we lost, but there were some bright spots."
Undrafted out of Oregon State, Moore went 10-13 as a starter in three seasons with Carolina, including 1-4 last year. He signed as a free agent with Miami at the beginning of training camp.
"One of the things that makes him attractive to me is that when the light goes on and you put Matt in the game, he tends to move your team pretty good," Dolphins coach Tony Sparano said.
On his first play in San Diego, Moore threw a 31-yard completion. That turned out to be their longest gain of the game, and they completed the drive by scoring their only touchdown.
It has been a sputtering unit with the much-maligned Henne, who has actually showed signs of improvement this season by throwing downfield more effectively. Even so, he ranks 24th in the league in passing efficiency and 28th in completion percentage.
And now his injury complicates the challenge of getting the offense on track.
"You always lose a beat, I think a little bit, when you lose your starting quarterback," receiver Brian Hartline said.
With Miami one of the NFL's four winless teams, Moore knows the situation is far from ideal.
"It's not what we want, but these guys are working, and we're hungry," he said.
Senior writer John Clayton covers the NFL for ESPN.com. Information from The Associated Press was used in this report.