Yes, it is possible, no problem.
Check the classifieds in the Straits Times every day, more precisely the section "houses for rent".
condo are always listed per district, houses are not.
Alternatively, go walk or drive around in the area you prefer and check if there are houses with a sign saying they are for rent, which are quite a few houses.
All the hype about rent being so expensive only means you have to put in a bit more effort, but for that money you can find a 3 bedroom house, for sure.
We ourselves just moved to a house in a prime district, no 15, in east coast, 3 bedroom, with a garden, freestanding bungalow, renovated, S$2.3k.
Time will come....