The introduction of a five-match minimum ban for racist abuse has the support of England's Professional Footballers' Association (PFA), the body's chief executive said on Wednesday.
The sanction is one of a number of proposals being discussed by the game's ruling bodies in the wake of a series of racism cases.
Chelsea skipper John Terry was given only a four-match ban for racially abusing QPR defender Anton Ferdinand while Liverpool's Luis Suarez received an eight-match suspension for his abuse of Patrice Evra.
PFA chief executive Gordon Taylor told Britain's Press Association: "It has not gone through yet but we are not opposed to it.
"We want there to be some consistency and to illustrate the seriousness of our approach to this issue."
The PFA also want all players and managers coming to England from overseas to have "cultural lessons" to make them aware of rules on discrimination under proposals to tackle racism. Until now only apprentices have been given such courses.
In another development on Wednesday FA independent director Heather Rabbatts insisted the game must respond to damning criticism of the handling of the Terry and Suarez cases.
Kick It Out chairman Lord Herman Ouseley has claimed there is "very little morality" at the top clubs and a lack of leadership and "a moral vacuum" in the game.
Rabbatts, appointed as an independent board member this year and a potential candidate to be the next FA chairman, said: "The issues that Herman Ouseley is raising are hugely important issues for the whole game and it has to respond to these challenges.
"There are a number of members from different parts of the game being consulted and we all have to rise to the current challenge.
"Despite the huge progress that has been made in tackling discrimination there is a need for renewed energy."