Cooper’s Forest were beaten at the City Ground by Everton in the Premier League on Saturday evening and are on a run of poor form.
Forest have lost four of their last five Premier League matches and questions are being asked about whether Cooper can survive further bad results.
The club stuck by Cooper last season, but could be tempted to make a change and if they do then Austrian boss Glasner will be the leading contender.
Glasner, 49, is currently out of work, having most recently been in charge of Eintracht Frankfurt.
He led Eintracht Frankfurt to success in the Europa League and is highly rated – and would be free to come in.
Glasner has been linked with Premier League jobs over the last 12 months and was mooted as a target for Tottenham Hotspur before they appointed Ange Postecoglou.
The Austrian tactician, who made over 500 appearances as a defender for Austrian side Ried in his playing days, would likely be tempted by a Premier League chance.
Nottingham Forest next face Fulham at Craven Cottage, before then hosting Wolves.