FA is looking into an incident between the pair when tempers flared and Memeti and Vidic were part of an all-in melee late in City's spiteful 1-0 A-League Men win over the Roar at AAMI Park on Tuesday night.
City forward Memeti, who is of Albanian heritage, is accused of calling Vidic, of Serbian background, a "gypsy", a term that has derogatory connotations in the Balkan region.
Vidic was seen remonstrating with Memeti at fulltime as tensions threatened to boil over and interrupt City coach Aurelio Vidmar's post-game interview on Network Ten.
In his own post-match interview, Memeti downplayed the confrontation and said Vidic was "a bit cut 'cause he lost".
Vidmar was adamant in his press conference on Friday he was not aware of what was going on.
"No, I just saw what was happening behind me. I had no idea what was going on," he said.
When asked about the situation, Vidmar played a straight bat, saying: "The process is with the FA."
When asked whether Memeti would remain available for selection while the investigation was underway, Vidmar said: "Yep."
It means Memeti, who started against Brisbane and is one of City's brightest young stars, will be expected to feature in Sunday's home game against Newcastle at AAMI Park.
When asked if he'd spoken with Memeti about the situation, Vidmar said: "No. No need to."
If there is sufficient evidence to support the allegations, Young Socceroo Memeti could face FA's disciplinary and ethics committee for the use of discriminatory language.
There is a precedent in terms of a sanction for the use of "gypsy" as a slur.
Now-Roar goalkeeper Dean Bouzanis was suspended for five matches in 2017, when he played for City, for directing the insult towards then-Victory star and Kosovo international Besart Berisha.
Roar chief executive Kaz Patafta confirmed the FA investigation on Thursday afternoon.
"There's an investigation by FA and we want to ascertain facts like every other club does," Patafta told reporters.
"The chair of Melbourne City has reached out and we've been in discussions.
"We take all matters, especially of this type of situation seriously, like any organisation does.
"But right now we need to ascertain facts, understand what's occurred, and then we'll take it from there."
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