He previously pleaded not guilty to the charge at a hearing on 10 September at Nottingham Magistrates’ Court.
Coote, who wore a navy suit and black tie, spoke only to confirm his name and enter his plea during the six-minute hearing in front of Judge Nirmal Shant KC.
He was sacked last year when comments made in a video about former Liverpool manager Jurgen Klopp in 2020 came to light.
The judge told Coote she was ordering a pre-sentence report to be carried out before sentencing.
Judge Nirmal Shant KC told the court: “You have pleaded guilty to a serious matter. Whether this means custody or not will be decided when all the information is before the court, which is why I have ordered a pre-sentence report.”
In August this year, Coote was given an eight-week suspension by the Football Association over the Klopp footage.
