Cotterill is believed to be Forest's favoured candidate to replace Steve McClaren, who quit the City Ground 10 days ago after just over three months in charge.
Pompey confirmed the 47-year-old was at the training ground as usual preparing for Saturday's clash with Barnsley, but are refusing to comment on reports Forest have made an official approach to speak to him.
Meanwhile, Cotterill's pre-match press conference, which usually takes place on a Thursday, has been moved to Friday morning.
Cotterill impressed while guiding Pompey comfortably clear of relegation trouble on a shoe-string budget last season, but they have taken just nine points from their first 10 games this term.
Former Barnsley boss Mark Robins and Aston Villa coach Kevin MacDonald have also been linked with the Forest job. Assistant-manager Rob Kelly will be in charge against Coventry on Saturday if no appointment is made in the meantime.