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.
Mourinho, who has lamented the grilling he gets from Italian media so much that reports have speculated he could quit in May, said he snapped because the journalist had been standing by the team bus for months despite his protests.
"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."
The colourful 46-year-old said there were no problems between himself and Moratti and indicated he would accept a punishment from the club for his outburst rather than a sanction from the league.
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.
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