HDB rent for around 1600 SGD

S$1600/month is the minimum you can find anything at. As usual, you don't get quality at low price, so expect (after a long search) a run-down flat in an inconvenient location (long commute time) and, if furnished, junk that can barely be used.
Better budget S$2000/month to get something reasonable.

Thank you beppi for the information.

I gone through propertyguru and could see some HDBs in even less price. After reading your post, I doubt if those are genuine.

Please suggest me some way to find better HDBs.

If it's cheap (below S$1200/month), it's probably a sublet room, not a whole unit. The ads are often not clear about that, so call and ask.
You have to go and have a look at the apartment and its surrounding to see if it's suitable for you or not. Go there by public transport, so you know how difficult it is and how long it takes.
You should then also check with HDB whether the landlord is actually the owner of the apartment, and whether he/she is allowed to rent it out. Don't rent an HDB illegally!
Also, most rents are negotiable, so ask for a discount of S$100 or 200!
Last not least, the more time you have for your search, the more likely you are to find a good place. Do not expect to find it in a few days or a week!
In my experience, property agents are mostly useless (and costly), so better try to search without them. They are also often not honest and place ads of non-existing apartments, just to lure you into engaging them for a (costly) search. So if an agent tells you " this apartment is already gone, but should I look for similar ones for you?" never say Yes, otherwise you have to pay him!

A reasonable 2 BHK  (2+1) unit near to Metro train station area with fully furnished would fetch $2000 (if you look near to city centre or Business district can fetch little more). PropertyGuru or any other agency their main target is to get clients in. So, they put few non genuine rental ad to attract people like you and when you contact them, they will say that the unit has already taken but they have other units to see. But it's true that rent has fallen significantly in last 3 years. It depends on where is your office located, your Budget and your accommodation priorities including to avoid traveling time. Far from metro station & Malls, and city centre or business district, the cheaper you get (Bus services are linked to every corner of Singapore so it's not an issue to go to your office using bus transportation though).

Thank you beppi and surya2k for all the suggestions.

I will be moving there may be in October. Any possibility of getting good HDBs in first 10 days? or Do I need more time? Also considering your suggestions I can increate my budget little more.