Mourinho will take over as Roma boss at the start of next season
The Portuguese manager will take over at Roma in the summer as he moves back to Italy for the first time since 2010.
And Conte, who has led Inter to their first Serie A title since Mourinho was there 11 years ago, is excited about his move to Roma.
Speaking on Italian show Le Iene, he said: “It’s great news for everybody, I wish him the best, except when he plays against Inter.”
The pair enjoyed a combustible relationship during their time together in English football with both exchanging verbal barbs on several occasions.
When asked if they will hug on the touchline, he added: “For sure, there is great respect between us.”
The announcement that Mourinho is joining Roma comes less than a month after he was sacked by Tottenham.
He previously coached in Italy with Inter between 2008 and 2010, enjoying one of the most successful periods of his managerial career.
Under his stewardship, Inter won two Serie A titles, a Coppa Italia, the Supercoppa and the Champions League.
He then left immediately after winning them a treble as he joined Real Madrid.
Roma have seriously struggled in Serie A this season with the club currently languishing down in seventh place.
No Italian club has won the competition since Parma way back in 1999.