The 44-year-old was brought to the King Power Stadium over the summer following the exit of former head coach Enzo Maresca to English giants Chelsea.
Cooper's relaxed management style has been a drastic change from the philosophy of Maresca, who sought to control every aspect of his side's play.
Since back-to-back wins over Bournemouth and Southampton at the beginning of October, Leicester have endured a four-game winless run across the league and EFL Cup.
As a result, the Foxes are currently occupying 15th spot in the Premier League rankings, just three points above Crystal Palace in the highest of the relegation places.
Leicester hand Cooper timeframe to save his job?
According to journalist Alan Nixon, relegation-threatened Leicester have set the timeframe in which Cooper will battle to save his employment.
The report claims that the Foxes board have decided to give the Welshman until the end of the calendar year to improve the fortunes of the East Midlands club.
It is understood that Leicester have already commenced the process of sounding out potential replacements for Cooper, including former Chelsea boss Graham Potter.
The Englishman has been out of work since departing from Stamford Bridge near the beginning of 2023, waiting for the right opportunity to jump back into management.
It is also believed that Ruud van Nistelrooy is in the frame to become the next Leicester boss following his impressive interim spell at Manchester United.
Cooper's crucial end to 2024
If the reports are true, Cooper will be afforded eight Premier League matches to save his position at the King Power, starting with the visit of Chelsea on Saturday afternoon.
Leicester's final two matches of the calendar year are against leaders Liverpool and second-placed Manchester City, so the Foxes will need to be productive in the five games previous.
The standout fixture of the bunch is the hosting of relegation rivals Wolverhampton Wanderers on December 22, when the fate of Cooper could be sealed.