Asked by reporters about Roma defender Mancini's behaviour in the aftermath of Saturday's 1-0 win, Gabriele Gravina said: "I don't have any comment other than that I have been informed that (disciplinary tribunal) prosecutors have opened an investigation. Checks are underway."
Italy international Mancini headed the only goal of a tense clash with Lazio to end Roma's two-year winless run against their local rivals.
Both he and Paulo Dybala, who supplied the cross from which Mancini scored the winner, celebrated the win with joyous fans, joining in with chants and waving flags.
Mancini grabbed one flag which depicted a black rat on top of Lazio's colours of white and sky blue, and charged along the running track in front of the Stadio Olimpico's Curva Sud, where Roma's hardcore fans stand.
His behaviour angered Lazio, whose captain Ciro Immobile criticised Mancini after the match.
"There are different ways you can celebrate, some people do it with style but other people not so much," said Immobile.
Mancini later apologised, claiming that he "didn't want to offend anyone".
"I took the first flag that they gave me... I didn't mean to disrespect anyone and I apologise. I just wanted to celebrate with our fans," Mancini said.
Mancini's celebrations were a controversial postscript to a typically colourful and tetchy derby in the Italian capital, where passions always run high regardless of what's at stake on the pitch.
Several hundred fans briefly fought near the stadium hours before kick-off before the scrap was broken up by police.
Mancini's winner ensured that Roma would stay fifth for another week, five points ahead of Atalanta who are at Cagliari on Sunday and also have an extra game in hand.
Serie A is leading the race for an extra spot in next season's Champions League, meaning a top-five finish could be good enough for Roma to qualify for Europe's top club competition for the first time since 2018.
