Football Association of Malaysia (FAM) secretary-general Azzuddin Ahmad expects the game against the nine-times European champions to take place on August 21 - in the middle of Ramadan where Muslims fast for the holy month.
However, Malaysian news agency Bernama said Azzuddin was discussing with national coach K. Rajagobal about playing at 2200 local time as Muslim players and fans can eat before sunrise.
Azzuddin also said he was hopeful refurbishments to the National stadium, due to start shortly, could be delayed by two months so that they could use the venue for Real game.
The Kuala Lumpur Football Stadium has been earmarked as a possible alternative.
The national team also play a friendly match on July 17 against Championship side Cardiff City, taken over by Malaysian businessmen Tan Sri Vincent Tan and Chan Tien Ghee last month.
"Playing Cardiff City and Real Madrid, especially, who have a list of world class players, will give my players valuable experience and world class competition," Rajagobal said.
The FAM have brought forward domestic fixtures to accommodate the arrival of Cardiff, who will also play a fixture against the under-19 team on July 15.
