Forest are currently on a run of just one win from nine games in the Premier League, and face relegation rivals Everton at the City Ground next on Saturday.
The pressure has risen on Cooper following a 3-2 defeat at home to Brighton & Hove Albion, where Forest struggled to create chances despite playing against 10 men for the final 20 minutes plus 10 minutes of added time.
Marinakis has spent heavily to try to meet his target of making Forest a top-10 Premier League team, but they are lagging behind that objective currently.
The club find themselves down in 15th, but they are eight points clear of the drop zone, aided heavily by Everton's 10-point deduction.
The Telegraph claims that the Greek billionaire still has absolute faith in Cooper, but has made it clear results must improve.
Upwards of £100m was spent over the summer, including breaking the club's transfer record to bring in Ibrahim Sangare from PSV Eindhoven, but Forest remain lingering near the relegation places.
The sale of Brennan Johnson to Tottenham Hotspur for £47.5m was not ideal towards the end of the window though, now combined with the fact that Taiwo Awoniyi will now miss up to four months following groin surgery.
Given that Forest's next three games all appear winnable — versus Everton, Fulham and Wolverhampton Wanderers — they are allegedly reluctant to make any changes during such a potentially pivotal period, heading towards the festive period.
Marinakis's faith in Cooper paid off last season, as the Welshman overcame serious doubts about his future to lead Forest to survival, after
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