League officials and Inter president Massimo Moratti are probing the incident outside the team bus after Italy's sports journalists' union complained.
"It's true I insulted one of your colleagues with a word I cannot repeat that was offensive. But it is not true that there was aggressive intent or physical contact," Mourinho told a news conference on Tuesday.
"I will not make a public apology because the situation was not public but private," added the Portuguese, whose Serie A leaders host Livorno in the Italian Cup last 16 on Wednesday.
"In front of him, like men, I will be able to talk with him and end this story. Maybe with a bit of humour - I expect a Christmas present from him."
Mourinho also said he would welcome a new striker in January to cover for Samuel Eto'o's absence with Cameroon at the African Nations Cup.
He mentioned Palermo's Edinson Cavani as well as Luca Toni and Goran Pandev, who have fallen out with their clubs Bayern Munich and Lazio.
"If we can have someone new in, good, if not it's still fine," he said.
