Tagovailoa suffered a concussion on September 30 after being sacked by Cincinnati Bengals defensive lineman Josh Tupou in the second quarter.
The 24-year-old lay motionless on the field for several minutes before he was placed on a backboard and stretcher.
Video showed Tagovailoa’s forearms were flexed and his fingers contorted – a sign that CNN’s Chief Medical Correspondent Dr. Sanjay Gupta said is a “fencing response” and can be linked to a brain injury.
McDaniel told reporters on Monday that Tagovailoa was recovering well.
“I’m not even really thinking about his timeline. As I said before, we’re just trying to get him as healthy as possible,” he said.
“We’re pretty much in a 12 to 24-hour reoccurring evaluation process, and he’s doing well.
“He was here today, but he is not ready to take the step to do some football stuff yet.”
Tagovailoa had suffered an injury in the previous game and was allowed to continue. He then played against the Bengals before being sidelined.
A review into the response to his injury concluded with a change to the league’s concussion protocols.
Under the new rules, players will be unable to compete if they are experiencing ataxia, which describes a lack of coordination caused by poor muscle control.
Bridgewater had replaced Tagovailoa for the next Dolphins game but was then sidelined himself after taking a heavy hit.
He was unable to return to the game because of the new concussion protocol that went into effect the same day, making Bridgewater one of the first players to be sidelined under the new rules.
Bridgewater suffered a blow to the head during his first snap of the game when he was tackled to the ground after throwing the ball.
The Dolphins tweeted that he was evaluated for injuries to both his head and elbow and later announced he was ruled out of the game.
“He had no symptoms today. He had no symptoms yesterday, but per the rule change, he is being treated as though he has a concussion,” McDaniel added.
“So he is in the subsequent protocol.”
The Dolphins face the Minnesota Vikings in its next game on Sunday with rookie signal-caller Skylar Thompson the most likely to take up the quarterback responsibilities.
However, despite the rotten luck, McDaniel is not feeling sorry for himself over the selection dilemma.
“It’s difficult but nothing that I don’t see as part of what I expect from myself and what I expect from the coaching staff, so you don’t need to shed any tears for me,” he said.