José Mourinho has told Claudio Ranieri his achievement at Leicester last season was bigger than all three titles he won in his two spells at Chelsea, and the people of the city will never forget him.

The Manchester United manager – who suffered a similar fate to Ranieri after winning the title in 2015 – thinks renaming the King Power Stadium in the Italian’s honour would be a fitting tribute to the manager who was relieved of his duties on Thursday, though he is not sure how much honour remains in football.

“We cannot be naive, we cannot go around believing it is the same game we had 20 years ago, even 10 years ago,” Mourinho said. “Everything is changing around and we must not be afraid to make people realise where we are in the industry we are in.”

Mourinho then joked of Chelsea’s manager: “I think Antonio Conte has to think about whether he really wants to be champion this year.”

Mourinho went on holiday to Brazil after being sacked by Chelsea, before watching a few Premier League games on television and thinking about his next step. “For me there clearly was a next step and there will be for Claudio too,” he said. “This happens to managers. We cannot make dramas about it. But what helped me was the knowledge the Chelsea supporters remain grateful for what I did for the club and I am sure that will help Claudio, too. Chelsea supporters do not forget what I did and in my opinion Claudio did even more for Leicester. What he did there was bigger than all of the titles I won at Chelsea and in 50 years’ time the Leicester fans will still know that.”

At 65, 12 years older than Mourinho was when he was sacked last season, there may not be too many top-flight situations open to Ranieri. Plenty of people thought he was too old and out of touch when he was appointed at Leicester in 2015, though he corrected that impression in some style.

“From my experience there are two things Claudio needs to know,” Mourinho said. “The first is that nobody can delete history. You cannot go to the laptop and press delete. And I can promise him also that nobody forgets. Leicester fans will always be positive about his time at the club. They will react in a positive way.”

Mourinho takes his team to Wembley for the EFL Cup final on Sunday afternoon, with the possibility of becoming the first United manager to win a trophy in his first season.

Sir Alex Ferguson used to consider any season that yielded silverware a success and, though the League Cup is the least of the three domestic prizes, Mourinho agrees it is getting harder to win anything in England. “In some countries it is easier and in certain countries it is really easy when you are at the right club,” he said. “In England every competition is difficult to win. I think even the League Cup is getting very hard because there are so many good teams around and everyone is hoping to end up with something.”