The Chelsea manager was flattered with comparisons to the Derby County and Nottingham Forest legend, was pleased for Southampton's Ronald Koeman and said he appreciated the comments from Roy Keane and Paul Lambert regarding an early handshake.
Clough brought success to both Derby County and Nottingham Forest - with his honours as a manager including two league titles, two European Cups and four League Cups as he transformed the fortunes of both clubs.
Warnock said of Mourinho: "I think he's the nearest thing to Cloughie. He's that type. He's a player's manager but he doesn't keep the players in his pocket.
"He says it how it is. He always wants his teams to play well. Tactically, in difficult games, he's always spot on."
Mourinho has had an illustrious career to date but said there is no real comparison with someone he described as a legend of English football, but said he was proud that a fellow manager would want to make those comments.
He told reporters: "I feel flattered with this comment that I've been compared to Brian Clough, but there is no comparison - he is a legend in English football.
"What happened with Nottingham Forest will stay forever - a big loss because he went so early. The legacy of Mr.Clough - it has no comparison."
Mourinho also made a joke about not wanting the manager of the month award. Despite leading his side to a five point cushion at the top of the table after seven games this season, the Chelsea boss said he was happy that Southampton boss Ronald Koeman received the award.
He said: "Ronald Koeman deserves the award. He's a great guy and a good friend.
"The second reason I'm happy is that the manager of the month always loses the next match."
Swansea City boss Garry Monk won the award for August but his side lost to Chelsea.
The Chelsea manager was also asked about comments from Roy Keane and Paul Lambert who said he had been disrespectful by trying to shake their hand before the end of their game last month. He said he would do it again, but appreciated their comments.