The Professional Footballers' Association say they will back proposals for a minimum five-match ban for racist abuse.
The sanction is one of a number of proposals being discussed by the game's ruling bodies, but has yet to be agreed by the Football Association.
Chelsea skipper John Terry was given 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.
The PFA said on their official Twitter feed: "The PFA have agreed proposals with @FA that 'racist abuse' should carry a minimum five-match ban."
PFA chief executive Gordon Taylor said: "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.
Meanwhile, FA independent director Heather Rabbatts insists the game must to 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, a lack of leadership and "a moral vacuum" in the game.
Rabbatts, appointed as an independent board member earlier this year and a potential candidate to be the next FA chairman, said Ouseley had raised important issues.
She 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."