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There is no law against foreign non-residents holding bank accounts in Singapore.
But most banks seem to require a local residence, or a local guarantor.
In any case you have to visit a branch with your passport or other ID for the identity check.

So you think that it is not possible to open an account online and even if I come to Singapor, I am not sure I'll find a bank which accepts to open an account for me, correct?

I think you should contact the banks of your choice and ask whether what you want to do is possible, or not.

Since the account is meant for business purposes: It is relatively easy for a foreigner to register and own a company here, which in turn can open a (business) account.
For this, you need to engage a incorporation consultancy, which can also provide the required resident director - all for a fee, of course.

No, I am talking about a personal account.
Any advice which bank could accept so that I contact them directly?

Thanks

No idea, but I think international banks (e.g. Citi) with higher fees might be more willing.

I hold the IPA approval and i am currently outside Singapore. Can i open a bank account based on my approved IPA letter ?

@ShBhardwaj As far as I know, you need a registered Singapore address to open a bank account (and online banking probably requires a Singapore mobile phone). As long as you have that, it does not matter where you physically are.

@ShBhardwaj DBS/ POSB accounts only, rest of the banks expect you to walk in with your passport.

Local contact number, Registered address needed as Beppi outlined.