European Professional Club Rugby (EPCR) has launched an investigation into comments made by Bastareaud, who was seemingly incensed by something Negri said late in Toulon's 36-0 European Champions Cup victory.
Bastareaud tweeted an apology after the match, saying: "I want to apologise for the way I reacted to the insults of the Italian player.
"I responded badly to his provocation, I am sincerely sorry to the people I have hurt."
Toulon followed the player's statement with a response of its own, defending the club's integrity while insisting the comments were out of character for Bastareaud.
"The Rugby Club Toulonnais insist that they have always defended the differences between people and called to respect them," Its statement read. "The RCT is convinced that Mathieu has made unfortunate comments following a state of nervousness, as could happen during a rugby game, and he is in no way homophobic.
"This verbal slip should not mean throwing away our captain, who has always defended the diversity between individuals."
If Bastareaud is found guilty of verbally abusing Negri, it could affect the France international's participation in the Six Nations, with Les Bleus starting their tournament against Ireland on 3 February.