Hello!
You could also consider looking at startups for your internship, especially since there is a dearth of software engineering talent in Singapore now. Try
PSDPY | Startup Jobs
Lithan Hall Academy also has a programme where they place you at an early stage startup for 12 months with regular salary, while giving you the opportunity to pursue a diploma in technopreneurship.
Do check it out:
Wanted: Entrepreneurial Talents
Hope this helps!