The Reds appointed their German gaffer last month and have enjoyed an undefeated run of six games since his arrival.
Rodgers, who almost guided to the team to Premier League glory in 2013/14, had come under increasing levels of pressure prior to his dismissal, which was confirmed after the 1-1 draw against Everton in the Merseyside derby.
And reports claim that the decision was made ahead of the game at Goodison Park, with Liverpool eager to lure Mourinho to club from bitter rivals Chelsea.
However, their plans were quickly thwarted by the Portuguese tactician’s reluctance to walk away from Stamford Bridge, which was needed due to the compensation fee that would have been due for his signature.
Liverpool instead moved for Klopp, who is already a fans’ favourite at Anfield.
The likelihood of Mourinho ever managing at Liverpool would appear to be slim, with large sections of the club’s supporters having been irked by his actions towards their team during both his spells at Chelsea.