Winston will not play in Week 12 against the Atlanta Falcons and will be re-evaluated next week.
"Until he's cleared, I have no say in it," Koetter said. "Jameis isn't cleared."
Winston has been battling a sprained AC joint in his right shoulder since Week 6 and was sidelined two weeks ago to rest. The original timetable for Winston was at least two weeks. He has not practiced with the team and received a PRP (platelet rich plasma) injection to accelerate healing.
"Ryan's done exactly what I thought he'd do," Koetter said. "Ryan made really good decisions. We didn't turn the ball over."
The NFL confirmed last week that it is investigating a female Uber driver's allegation that Winston grabbed her crotch area in March 2016 in Scottsdale, Arizona. Winston has denied those allegations, stating that he was not the only passenger in the vehicle.
The driver has retained attorney John Klune, who also represented the woman who accused Winston of sexual assault at Florida State in 2012.