He added that Tagovailoa will not travel with the team for Sunday's game at the New York Jets nor would he be going on injured reserve at this time.
"He's been diligently going through the process," McDaniel told reporters. "Right now he's still in the protocol obviously. There's several outside specialists that we're also utilizing and we'll just take it from there.
"But happy that we get to see him every day. It's nice when I walk down the hallway and I hear, 'What up, beast?', which is, for whatever reason he calls me beast all the time. I don't think I give off he beast vibe."
When a player is added to the injured reserve list it means he is ineligible to play for at least the next four games.
Tagovailoa was carted off a the field last week after his head slammed onto the turf when taking a sack during a prime time game against the Cincinnati Bengals.
The quarterback's arms appeared to seize up immediately after that hit and he remained on the field for about seven minutes before being taken to hospital where he was diagnosed with a concussion.
That incident came four days after Tagovailoa looked disoriented after hitting his head on the ground during a game against the Buffalo Bills.
He was cleared to return to the Buffalo game after being evaluated for a concussion by an unaffiliated neurotrauma consultant but his treatment has since put the NFL's concussion protocol under scrutiny.
The NFL and the NFL Players Association have since said in a joint statement that modifications to the concussion protocol are needed to enhance player safety.
