Can apply for work visa while travelling in Singapore?

No . you can't apply for a visa while you are visiting.
The rules are very strict in Singapore .
Don't break any rules when you are in Singapore.

The above poster rajrana1981 is wrong:
It is possible and allowed to look for a job and attend interviews (just not work) while in Singapore on a tourist visa (SVP). After an employer offers you a job and you signed the contract, they can also apply for your work visa while you are in Singapore.
And if the work pass is approved while you are still in Singapore on an SVP, you can even get the work pass issued and start work without having to leave the country.
However, you should note that you normally get a 30 days SVP (and under certain circumstances this can be extended to 89 days on application at ICA) and it is unlikely that all the above (looking for and applying for jobs, attending interviews, getting an offer, salary negotiations, signing of contract, application for work pass, approval and issuance of work pass) can all be completed in 89 days. These things typically take longer. Thus you will probably hav to return to your home country temporarily.

So beppi you mean everyone can come on tourist visa and apply . for jobs ?
Regards