The pair appeared to spit at each other during Wednesday's Premier League game at St James' Park.
Referee Anthony Taylor spoke to Evans and Cisse after the first-half incident, but neither was booked.
The Football Association says it is waiting for Taylor's report before deciding whether any action is needed.
Last season, George Boyd was given a three-match ban for spitting at Manchester City goalkeeper Joe Hart.
But from this season, FA disciplinary guidelines dictate that the penalty for such an offence is double that.
Cisse's punishment could be even greater, given he was sent off for violent conduct in December for elbowing Everton's Seamus Coleman.
FA guidelines indicate Cisse could receive an additional one-match ban.
A number of ex-players believe Evans and Cisse should be punished.
Former Newcastle midfielder Dietmar Hamann described the acts as "not acceptable" and "disgusting", while former Manchester United defender Phil Neville added: "Both those players will be embarrassed."
Speaking on BBC's Match of the Day, Hamann added: "There are kids watching. Something has to be done. The behaviour towards each other and the referee is deteriorating on a weekly basis."
Former Magpies midfielder Jermaine Jenas told BBC Radio 5 live: "I am completely disgusted. The game does not need to see this."
Television replays appeared to show Evans spitting towards Cisse, who was on the ground.
The Senegal forward then appeared to spit in the direction of Evans.
Neither Newcastle manager John Carver nor Manchester United boss Louis van Gaal said they saw the incident.
"I can't comment on it," said Carver, whose side were beaten 1-0. "I just know there was a fracas on the halfway line."
Van Gaal said: "I don't think Jonny Evans is a spitter. Maybe spitting on the floor, but we were on the bench and you cannot see from there."
Manchester United defender Jonny Evans and Newcastle United striker Papiss Cisse could face six-match bans if found guilty of spitting.