The Portuguese fired a jibe at the former Lazio and Pescara boss, revealing he does not know about anything that the 65-year-old has done during his coaching career
The 65-year-old, who took over from Luis Enrique at the Stadio Olimpico, had lashed out at Mourinho in 2009, describing the Portuguese as a "mediocre coach".
And in an interview with France Football earlier this week, Zeman criticised the defensive approach of Mourinho's Inter team, which won the Champions League in 2010, saying that its focus was on not letting their opponents play.
Mourinho has now reacted to Zeman's criticism, responding through the Twitter account of his spokesperson, Eladio Parames.
"I am a mediocre coach? Ok! I respect every opinion," Mourinho stated. "Zeman? I do not know him. Where does he play? He is a coach? Sorry, I did not know that.
"Now that I am on holiday I will look him up on Google to find out who he is and what he has won."