A shelter-in-place order has earlier been issued at Azteca Stadium because of adverse weather.
With regards to delays caused by severe weather, Fifa has no power to make its own rules - it must adhere to the advice of local authorities.
In the United States, recommendations of the National Oceanic and Atmospheric Administration (NOAA) are used.
The NOAA says if any lightning strike is detected within eight miles of a stadium, the game has to be stopped. The rules are the same in Mexico.
Fifa said in a statement: "The safety and security of all individuals is Fifa's priority."
Sources told BBC Sport on Friday that Fifa had been set to reschedule the fixture to an earlier kick-off time, but news of the proposal angered both English and Mexican officials.
The Football Association requested time to review the weather forecast in more detail.
As talks went on, concerns over the impact on player preparation, fan travel and the logistics around moving the staging of such a huge game were discussed.