Is there a way for the the wifi router to know how many wifi enabled devices are within range even if they are not connected ? Is this the same technology as my laptop/mobile phone knowing all possible wifi routers in an area and listing it according to signal strength ?
(Judging by the phrasing and triviality- you can know I have no idea whatsoever about wifi networks and stuff)
Simple answer: No.
Your mobile knows the APs around it because it's listening for beacons. (and actively probing its list of known APs) For an AP to figure out what's around it, it would have to constantly listen on every channel to pick up traffic. That's better known as monitor mode -- something air-snort does.
While is it probably not possible (or at least not easy) to know the set of devices in range, it is possible to know the set of devices that you can hear (which is not the same thing — you might hear them but they might not hear you, or they might be in range but not speaking). This is done by putting the interface into "monitor mode", where it passes to userspace all frames that it hears. (Under Linux, at least, most hardware supports simultaneous AP and monitor mode).
This is of course highly OS and hardware dependent, and using the information may require a fair amount of hacking.
