After a two-day meeting in Zurich, the committee approved the idea, which does not need the assent of the game's law-making body, the International Board.
Andreas Herren, a spokesman for football's world governing body, said: "This decision comes under Fifa regulations for competitions. So if a national association wants to organise its cup competition using this method, they are free to do so. Uefa, for example, could introduce this at the next European Championship."
In other wide-ranging proposals to make the game more attractive, the committee told Fifa that players scoring a goal by deliberate handball should be sent off, that the back-pass rule should be extended to all parts of the body and that the goalkeeper should be allowed to move along his line when facing a penalty. Some of the items will be discussed when the International Board meets in Belfast on 1 March.
Herren added: "Some of the items on what we have called the referees' shopping list can be activated immediately, like the penalty kicks before extra time, and some of them need to be discussed by the Board, but they are all being introduced to make the game more attractive."Reuse content