The 18-year-old picked up 12 medals at the SEA Games earlier this month, including seven golds, to become the most decorated athlete at the 28th edition of the biennial event.
The next stop should be the world championships which begin on July 24 in Kazan, Russia, but Quah is scheduled to begin two years of full time service within a fortnight, leaving head coach Sergio Lopez in the dark.
"The strategy for the men's (medley) relay team is uncertain," Lopez told local media at the ongoing national championships.
"Hopefully, we will get a deferment. If we don't, we will have to forget about the relays. It is as simple as that."
Singapore media said talks were ongoing between local Swimming Association officials and the Ministry of Defence to defer Quah's service until after the Rio de Janeiro Games next year.
Local media said the ministry could defer service in "exceptional circumstances" for athletes who are capable of winning Olympic medals.
Quah, who won the 100 metre backstroke and butterfly at the national championships on Friday, has already clocked the Olympic qualifying time for the 200m butterfly.
In 2013, Quah's team mate Joseph Schooling was granted a deferment from national service until after the Rio Games.
The 20-year-old, who qualified for the 2012 Olympics, won nine golds at his home SEA Games earlier this month after taking Asian Games gold in the 100m butterfly last year. Like Quah, he has already achieved Olympic qualifying times for the Rio Games.
(Writing by Patrick Johnston; editing by Amlan Chakraborty)
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