Guardiola made headlines when he held six fingers up towards Liverpool fans to remind them of how many Premier League titles he had won.
Mourinho made a similar gesture during the final days of his tenure at Manchester United, as he held three fingers aloft towards Chelsea and Tottenham fans.
Given United sacked Mourinho not long after the gesture, Guardiola was asked after the Liverpool defeat if he felt he'd suffer a similar fate to the Portuguese manager.
"I hope not in my case... He won three, I won six... but we are the same like that," Guardiola said.
Guardiola added the gesture 'was just to make our fans feel that what we have done is extraordinary' and to 'prove that we are an incredible football club.'
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Word of Guardiola's comments reached Mourinho in Istanbul and, rather unsurprisingly, the Fenerbahce boss was all too happy to respond.
"Guardiola said something yesterday," Mourinho said.
"He won six trophies and I won three, but I won fairly and cleanly.
"If I lost, I want to congratulate my opponent because he was better than me. I don't want to win by dealing with 150 lawsuits."
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Mourinho was referring to the 115 charges brought against Manchester City by the Premier League relating to alleged breaches of Financial Fair Play (FFP) rules.
Their alleged offences, between 2009 and 2018, coincided with the club blossoming into the dominant force of English football.
City won the Premier League three times during that period in question - in 2012, 2014 and 2018.
The club deny all charges and an outcome is not expected until 2025 at the earliest.
Luckily for Guardiola, the pressure has eased somewhat after the Liverpool defeat as City got back to winning ways against Nottingham Forest on Wednesday.
Goals from Bernardo Silva, Kevin De Bruyne and Jeremy Doku ended City's seven-game winless run as they beat Forest 3-0.
However, Guardiola faces a major battle if he is to steer City to a seventh Premier League title as league leaders Liverpool sit nine points ahead.
City will look to build on their momentum when they take on lowly Crystal Palace on Saturday.