The Italian and Portuguese tacticians have clashed several times since Conte took charge at Stamford Bridge, Mourinho branding the Blues boss a 'clown' and bringing up his previous match-fixing scandal when managing Juventus.
Conte responded by calling Mourinho a 'little man' and 'senile' while admitting that there was a problem between the two managers.
Ahead of this Sunday's meeting between Chelsea and United at Old Trafford, it was expected that both men would use their respective pre-match press conferences to continue their feud.
Instead, Conte said he was keen to put their spat behind them, a sentiment echoed by former Blues boss Mourinho later on Friday.
'I'm not interested in this topic. Both said something in the past, but we stop,' said Conte. 'For me, the situation has stopped.'
Meanwhile, when Mourinho was asked about Conte, he said: 'I told you before I'm not going to speak about it. Not at all.
'That's not the point. Very good manager, fantastic team and that's what is important for me. Just that.'