Pressure on the 44-year-old cranked up a notch on Sunday afternoon, when the Foxes suffered a 3-0 defeat at the home of Manchester United in the Premier League.
Most of the damage was done in the first period by the Red Devils, who were two goals ahead at the half-time whistle courtesy of a Bruno Fernandes effort and an own goal from Victor Kristiansen.
Fighting to restore parity in the contest, the visitors to Old Trafford were hit again late on, with Argentina international Alejandro Garnacho netting off the bench.
Cooper's troops are currently occupying 15th spot in the Premier League standings after 11 top-flight fixtures, sitting three points above Crystal Palace in 18th.
Moyes, Potter interested in Leicester job?
According to Football Insider, two high-profile British managers are eyeing up a return to coaching at the King Power Stadium in the near future.
The report claims that both Moyes and Potter are interested in taking the reins of newly-promoted Leicester should Cooper exit the club this season.
It is understood that the Foxes hierarchy have been mightily close to dismissing the Welshman, with a last-gasp Jordan Ayew equaliser at Ipswich Town earlier this month saving the manager's job.
There have been serious concerns over Cooper's laid-back approach in the East Midlands, with the players struggling to adapt following the departure of Championship-winning boss Enzo Maresca to Chelsea.
It is believed that the first-team crop of the Foxes are yet to be fully convinced by the tactics and methods of the 44-year-old as the harsh winter months draw nearer.
Moyes, Potter to enjoy Premier League returns?
For a club who look set to battle with relegation this season, Leicester would be lucky to have either Moyes or Potter in the managerial hotseat.
Moyes has been out of work since leaving his post at West Ham United at the conclusion of the 2023-24 term, with the coach winning the Europa Conference League with the Hammers.
Also a former manager of a London-based side, Potter has experience of coaching one of the country's biggest clubs in the form of Chelsea before leaving in April 2023.
With Cooper hanging onto his job by a thread at the King Power, Maresca and Chelsea will visit in the Premier League on November 23 following the international pause.