Antonio Conte branded Jose Mourinho a "little man" after the Manchester United boss continued his spat with the Chelsea manager with a jibe about match fixing.

The Premier League rivals have been involved in back-and-forth verbal sparring in recent days after it was suggested Mourinho had aimed a dig at Conte when he said he prefers to act in a "mature" manner on the touchline, rather than "crazy" or like a "clown".

Conte responded ahead of Chelsea's trip to Norwich City in the FA Cup by suggesting his Stamford Bridge predecessor was suffering from memory loss having been guilty of exuberant antics on the sidelines.

After United's 2-0 Cup win over Derby on Saturday (AEDT) Mourinho replied by saying: "What never happened to me and will never happen is to be suspended for match-fixing".

Conte served a four-month ban in 2011 but was later acquitted, and he says Mourinho's latest comment is uncalled for.

"It is very difficult to answer this type of comment because I think when a person's target is to offend, to insult another a person, I think that you are a little, little man," the Italian said after Sunday's (AEDT) 0-0 draw at Carrow Road.

"I think that we all know him very well from the past but he is always the same.

"This is his way, it is not a surprise for me. I repeat, when you insult or offend another person you are a little man, and I think he is a little man.

"Life will go on, I'm not worried about him. For sure there is a good opportunity when we play Manchester United to clarify in a room, me and him in a room."

After the game with Norwich, Conte continued to hit back at Mourinho with another salvo.

"I consider him a little man, I consider him a man with a very low profile," the Italian said.

"There is a story to speak for him and me. You can change the story, but you have to know the story very well before hurting another person. In the last period, he's suffering a bit of amnesia."

Conte went further, questioning Mourinho's show of solidarity to Claudio Ranieri after the Italian's sacking by Leicester City in 2017, when he wore the initials 'CR' on his shirt.

"I remember for example, a stupid example with Ranieri, when he offended Ranieri for his English," Conte said. "Then when Ranieri was sacked he put on a shirt for Ranieri.

"You are a fake. I think you have good consideration for a person or not. It doesn't change your opinion to be more sympathetic or not.

"If you want to fight a person, you try to kill the person, and then after two years you try to help this person, because maybe it's good for you, your profile."