The world governing body's new anti-racism task force also wants an official at stadiums with the specific job of identifying acts of discrimination, and for countries and clubs across the world to provide a "concrete action plan" to combat the problem and to implement sanctions "in a harmonized way."
"We have a special responsibility in the way we can impact football and society," said FIFA Vice-President Jeffrey Webb, the head of the task force that met for the first time Monday in Zurich.
The proposals were included in a draft resolution that will be presented at the FIFA Congress in Mauritius at the end of the month.
FIFA President Sepp Blatter set up the task force after AC Milan midfielder Kevin-Prince Boateng led his teammates off the pitch when he was racially abused during a friendly against Italian fourth-tier side Pro Patria in January. It was the latest in a spate of racial-abuse cases among players and fans to blight the sport in recent years, including high-profile incidents that led to the suspensions of Chelsea defender John Terry and Liverpool striker Luis Suarez in the Premier League last season.
Boateng and fellow players Jozy Altidore and Serey Die — internationals for the United States and Ivory Coast, respectively — are on the task force. Boateng and Altidore didn't attend Monday's session because of club commitments.
Primarily focusing on the application of sanctions for racism and discrimination at its first meeting, the group is proposing a two-stage warning, ranging from fines and matches played behind closed doors for first or minor offences to more radical punishments like points deductions or relegation for repeat offenders or more serious offences.
Having racism observers stationed at stadiums, the task force said, would ease the pressure on referees and facilitate "the availability of evidence, which is not always easy to obtain, for the disciplinary committees to take decisions."
FIFPro Secretary General Theo van Seggelen and Yury Boychenko, chief of the anti-discrimination section at the United Nations Human Rights office, were among the 14 other people present at the meeting.