The leaders, two points above Roma, visit Siena on Sunday on the final day of the league season while their title rivals travel to Chievo.
Inter coach Jose Mourinho has been trying to wind up Roma in recent weeks in his inimitable style, joking Ranieri's side would pay Siena to win among other jibes.
Ranieri is not impressed and has had enough of the man who succeeded him at Chelsea and who, according to media reports, could now be heading to Real Madrid.
"Clearly I'm very much in his heart because he talks about me often. Honestly I don't care what he thinks or says, in fact, he bores me," Ranieri told a news conference.
Mourinho, whose side meet Bayern Munich in the Champions League final next weekend, hit back with typical panache.
"The boredom of Ranieri? What is the boredom of Ranieri?," asked the Portuguese in a statement. "I am educated and I only know The Nausea by Jean-Paul Sartre, a philosopher, a Nobel Prize winner, but also a great football fan."
Roma captain Francesco Totti met actor Russell Crowe, of the film Gladiator, inside Rome's Colosseum for a publicity photo shoot and Ranieri was keen to take the analogy further.
"We still have lots of nervous energy and want to satisfy our fans - they are our true gladiators. We want to reward our fans with one last triumph," Ranieri added.
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