Coote appeared in court on Tuesday in connection with an allegation relating to a category A video, the most serious kind, recovered by police back in February.
The 43-year-old, who was sacked after a video revealed controversial comments made about former Liverpool manager Jurgen Klopp, spoke only to confirm his name and entered his plea during the hearing in front of Judge Shant KC.
Coote was charged in August with making an indecent image of a child, and he previously pleaded not guilty to the charge at a hearing on September 10th at Nottingham Magistrates' Court.
As reported by the BBC, Coote wore a navy suit and black tie and the judge told Coote she was ordering a pre-sentence report to be carried out before sentencing. He was told he must appear in court again on December 11th after pleading guilty.