Just like any other foreigner, an Indian can also apply for SPR. However, the outcome of the application depends on several factors. Applying is easy, but the chances of approval depend on many factors.
Please also note that to apply PR in Singapore, you must fall in one of the eligible categories. One of the common path is to stay and work in Singapore and then apply under PTS scheme.
If you are thinking of applying for Singapore PR as a complete foreigner while staying in India then unfortunately there is no such scheme available.