The 23-year-old was suspended in May when “traces of a banned substance” were found when Baxter underwent Football Association testing.
Baxter denies any deliberate wrongdoing and put his case to the FA on Friday, with the outcome expected after the weekend.
A club statement read: “The club can confirm that Jose Baxter had his personal hearing on Friday morning in relation to traces of a banned substance being found in a sample following a routine Football Association out of competition drug test.
“The outcome of the hearing is expected by the middle of next week.
“Sheffield United will not be making any further comment at the present time.”
Blades boss Nigel Adkins, who was appointed after Baxter’s suspension, travelled down to the FA’s headquarters to attend the hearing and will offer his midfielder his full support.
“He has been training with us full on, his attitude has been spot on,” Adkins said. “I will be there in a supportive manner.
“We are there to support him, discipline is so important at the football club and we are there to educate as well.
“All the players need to understand that the players are role models moving forward. I can’t affect what has happened in the past, I can only affect the future so it is important from my point of view that I am there.”