Paul Williams is in charge of Forest until the end of the season.
“Nothing was gauged or organised. It was a chance meeting,” said McGovern.
Cotterill, 51, has been out of work since leaving Bristol City in January, having been sacked 256 days after he led the club to promotion as League One Champions – the Robins’ first league title since 1955.
Talking to BBC Radio Nottingham, Forest’s two-time winning European Cup captain McGovern continued: “The first person I bumped into when I got to the directors’ room was Steve Cotterill. Obviously I’d known him since his days at Forest, although he was only there for a short period of time, and it was casual conversation.
“When Fawaz arrived, he wanted to say hello. Steve happened to be at the game, it would be impolite not to say hello and have a conversation.”
Forest have taken just one point from 12 since Williams took over from Dougie Freedman in March.
Tuesday’s defeat was the Reds’ eighth in 10 games and leaves them 17th in the table, nine points above the relegation places.