The concerning situation quickly escalated and eventually got so ugly that Roma's team manager was left with no option but to call the police to intervene.
Police are working to identify around 15 people involved, sources said.
Fans are furious with the 23-year-old, who has put in a transfer request after falling out of favour at Jose Mourinho's Roma.
Mourinho did not call Zaniolo up for Sunday's 2-1 defeat at Serie A leaders Napoli.
A banner, meanwhile, was hung outside Roma's Trigoria training facility overnight calling on "cowards, profiteers and men of little account" to be sent packing.
Roma have reportedly denied an approach from English Premier League club Leeds United for the out-of-favour attacker.
According to Filippo Biafora of website Il Tempo, Leeds have made a modest loan offer for Zaniolo until the end of the season, given the player’s tense situation at his current club.
Roma, however, is believed to have promptly rejected the English side’s proposal, instead making it clear that any deal for Zaniolo will preferably be permanent.
The Italy winger has been linked to potential moves to AC Milan or Bournemouth, the Premier League side reportedly having made an offer of 28 million euros plus seven million in bonuses for Zaniolo, plus 10 per cent of an eventual sell-on fee.
Milan are reportedly willing to bid much less, although the player is said to prefer a move to the Serie A champions over a transfer to a team that is currently third-bottom in the English top flight.
ANSA
