"When we developed FF3, the volume of content in the game was so huge that the cartridge was completely full," he says, "and when new platforms emerged, there simply wasn't enough storage space available for an update of FF3, because that would have required new graphics, music and other content. There was also a difficulty with how much manpower it would take to remake all of that content." - Hiromichi Tanaka
"When we developed FF3, the volume of content in the game was so huge that the cartridge was completely full," he says, "and when new platforms emerged, there simply wasn't enough storage space available for an update of FF3, because that would have required new graphics, music and other content. There was also a difficulty with how much manpower it would take to remake all of that content." - Hiromichi Tanaka
Thanks to Eurogamer.net.
I personally don't fully understand this, but I guess it makes sense why they don't remake it for PlayStation.