Yeah, it's called a Visitor Seeking Employment in Singapore (Long Term). There is, however, a PEP, which needs to be able to prove a previous salary in excess of S$7000/mo. Should you be able to furnish three years tax returns showing that kind of income, should be easy to get one of those.
With regard to the former see this link for the full text:
http://www.ica.gov.sg/page.aspx?pageid=172&secid=171
A few points to highlight though as it would seem you may have missed them:
Overview
Foreigners seeking employment in Singapore may apply for a one-year (non-renewable) Visit Pass via e-VP or at the Counter.
Documents Required
For Online Applications via e-VP
Holder of foreign issued educational certificate is required to obtain the Employment Pass Eligibility Certificate (EPEC) from Ministry of Manpower and submit his/her application via e-VP
For Applications at the Counter
Holder of educational certificate issued by the school listed below may submit his/her application at the Counter.
This means only certain Singapore school that are vetted by the Government.
In all cases you must have a local sponsor that is either a Citizen or PR.
The problem is, unless you when to a local School and graduated, you MUST obtain an EPEC first.
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