A Scottish Football Association charge against Gardyne has been dropped.
The 35-year-old had been accused of breaching an SFA rule which states that individuals should not use "threatening, abusive, indecent or insulting words or behaviour".
The PA news agency understands the case was shelved because of insufficient evidence with no witnesses prepared to speak at a planned virtual hearing.
Gardyne denied saying anything discriminatory during the Scottish Premiership clash on December 6 amid accusations that he had used a homophobic slur.
The former Dundee United and Kilmarnock player was booked by referee John Beaton for using foul and abusive language towards a grounded Morelos during his side's 4-0 defeat.
"Look, there's no place for it," Gerrard added. "There's a campaign for this kind of stuff to get it eradicated out of the game. We want to be at the forefront of backing these campaigns."
However, Gardyne's agent, Tom Callaghan, later insisted the only phrase the player used was to call Morelos a "f***y".
It is understood there was no other comment which was picked up by the match officials or by the television microphones.
County took no action against him following an internal investigation but the SFA announced on December 31 that the player had been issued with a notice of complaint.
A disciplinary hearing was scheduled for January 21 before being moved back seven days.
But the disciplinary updates page on the SFA website now states that the notice of complaint has been "withdrawn" prior to the hearing date.
Gardyne's club said in a statement: "Ross County FC today welcomes the SFA's decision to withdraw the notice of complaint served to Michael Gardyne.
"We now consider the matter closed and will be making no further comment."