Mourinho has clashed with his Chelsea successor in the past and seemingly reignited the feud when he appeared to label Conte a "clown" for his actions on the touchline.
Conte responded by suggesting that Mourinho might have "senile dementia", leading Mourinho to reference a match-fixing accusation which Conte was eventually cleared of during his time in charge of Serie B side Siena eight years ago.
The Italian believes that Mourinho's comments prove that he is a "little man", and insists that he is looking forward to settling their differences when Chelsea and United next meet.
"I think it's difficult to answer this type of comment because when a person, their target is to offend and insult another person, [it means] you're a little man," Conte told reporters.
"We all know him very well. But it's always the same. This is his way. It's not a surprise for him. I think he's a little man. Life goes on. I'm not worried about him. There is a good opportunity when we play against Manchester United for me and him to clarify [the issues] in a room.
"When you tell something, you must take the responsibility. If you try to speak and then keep the situation general you must have a big personality, big balls, to tell this."
United and Chelsea are not due to meet again until February 25 at Old Trafford.