NTU and NUS do not specify in their admission page that the candidates must be from a local U/Ivy league university. You will never know if you never try.
From what I know, competition for a place in NTU is very intense as there are many people who have applied but got rejected (i.e. As many as 1166 candidates applied for MSc Info Studies, Info Systems and Knowledge Mgmt in 2011, only 121 were accepted into Info Systems, 83 for Info Studies and 74 for Knowledge Mgmt). There is a rising trend of ppl enrolling in Master programmes these days, the number of applications will just increase over the years (while the number of places for the programmes will not get much increase as I believe our government does not want to flood the street with even more graduates) as university graduates are almost everywhere on the street and Master degree is perceived as being a notch higher than Bachelor degrees.
In the programme I enrolled, many of my classmates are either local grads or students on scholarships. I did not come across classmates who are graduates from private Us but from the posts here, it seems like there are a few who made it through the rigorous enrollment process. Chances are slim for private U candidates but that doesn't mean no chance. As long as u have excellent academic results and a few years of relevant work experience then just give it a try. Like I mentioned previously, you will never know if you never try. Good luck, may the force be with you!