The La Liga giants are considering setting up an academy in the city-state and could bring youngsters to Madrid to train under their coaches.
"We've been talking to our partner here, (events company) Centurion, about that... to have the chance to play in Singapore," Real's international sponsorship manager Alfonso Roberes De Cominges told Channel News Asia on Monday.
"And not only to play a match but also to run different activities related to football through Centurion, as academies, as camps and as clinics, and also to strengthen our relationships with all the football clubs as well in Singapore."
Real had planned to play an exhibition game in Singapore as part of a pre-season tour in August but that looks unlikely as the venue is to be used for the national day parade.
The nine-times European champions first visited Asia on a pre-season tour in 2003 with stops in Thailand, Japan, China and Hong Kong.
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