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The champions play Manchester United at Old Trafford on Saturday, with the two managers having clashed in the past.
Mourinho called Ranieri "a loser" after replacing him at Chelsea and also insulted him while Inter Milan boss.
Ranieri said: "Mourinho is a fantastic manager, intelligent, clever. "[The issues] were a long time ago."
Mourinho replaced Ranieri at Chelsea in 2004 and said that the club considered the Italian to be "a loser", before the pair repeatedly fell out while both managing in Serie A.
The Manchester United boss won the treble with Inter at the end of his three-year spell 2010, with Ranieri in charge of Juventus and Roma during that period.
Mourinho criticised Ranieri's command of English, said he was "almost 70" when he was 56 and again questioned whether he had the mentality to win titles.
But Ranieri said any complaints were "prehistoric, not now."
"It [their relationship] is fantastic, very good, no problems," he said.
"Why? Do you remember in the summer when we had the Soccer Aid, I managed the Rest of the World team against Jose's English side.
"Maybe he has to offer me a good red wine. I love red wine and if he offers I will go and drink it with him [after Saturday's game]."
United ended a run of three defeats with a win at Northampton in midweek, after which Mourinho called his critics "football Einsteins".
Mourinho - who won his third and most recent Premier League title with Chelsea in 2015 - saw his team heavily criticised after defeat at Watford last weekend.
He told MUTV: "We had a bad week. I know that some football Einsteins, they tried to delete 16 years of my career and delete an unbelievable history of Manchester United and focus on a bad week and three bad results.
"But that's the new football - it's full of Einsteins.
"I can understand completely the disappointment for the fans with the last week, but I'm sure, back at home, they will be behind the team like they always are."
United captain Wayne Rooney has also been criticised for his recent form, but he told MUTV: "I don't really listen to what a lot of people out there are saying, because a lot of it is rubbish."
Leicester manager Claudio Ranieri says Jose Mourinho "is a fantastic person" and any issues between the two are "prehistoric".