Tagovailoa was taken out of the game in the third quarter after suffering his latest head injury as he dived into a tackle searching for a first down in Thursday's 31-10 defeat at home to the Buffalo Bills.
The 26-year-old was down on the floor for several minutes after the hit from Bills safety Damar Hamlin but left under his own power, hobbling slightly as he talked to team staff.
The quarterback suffered two concussions - along with other scares - during a 2022 season which threw his future in the game into doubt.
But he played without any noticable issues throughout last season only to see the concerns return in week two of this campaign.
The concern is that with each concussion the risks grow of the kind of serious long term brain problems that have afflicted players in the past.
"That’s it… NFL, go ahead and do the right thing,” retired former Dallas Cowboys wide receiver Dez Bryant wrote on X after the incident.
"Tua has had entirely way too many concussions. He needs to retire for his longevity health concerns," he added.
Former Denver Broncos tight-end Shannon Sharpe, now a prominent television pundit, agreed that Tagovailoa should call it a day.
"Really hope Tua is ok, but he’s gotta seriously think about shutting it down," said Sharpe on X.
"I hate saying this. His concussions are getting worse and worse, and he’s a young man with his entire life ahead of him," he said.
On Friday, Las Vegas Raiders coach Antonio Pierce said if he were the player's coach he would make it clear that he should quit.
"I'll be honest, I would tell him to retire. It's not worth it. It's not worth it," he said, noting this was the third such concussion.
"It's scary, you could see right away the players' faces on the field, you could see the urgency to get Tua help," he said.
But Tagovailoa's actual coach, Mike McDaniel, said it was not the right moment for him to broach the subject of retirement.
"It would be so wrong of me to sniff that subject. It's more in line with actually caring about the human being. You're talking about his career. His career is his.... Bringing up his future is not in the best interests of him. I would plead with everyone that generally cares that that should be the last thing on his mind," he said.
McDaniel said on Thursday, in the immediate aftermath of the injury, that evaluations of the injury and questions over Tagovailoa's return should be left to medical experts.
Some have questioned whether Tagovailoa was wise to have leaned into the challenge rather than taking the safer option of sliding to avoid contact.
But JJ Watt said he couldn't blame the quarterback from going as far as he could to make the first down.
"It is a bit of a double-standard in my opinion, everyone wants to see modern-day gladiators but they don't want the guilt that comes along with it," he said.
