I need to implement an app that monitors inbound/outbound connections by different apps on iPhone. my app is going to run in background using apple\'s background multitaskin
Generally, I agree with Suneet. All you need is network sniffer.
You can try to do partial port of WireShark (it's open source and it works on MacOS) to iOS. Both iOS and OS X share most part of the kernel, so if it's not explicitly prohibited on iOS, it should work for you.
WireShark is quite big product, so you may be intersted to look for another open source network sniffer which work on OS X.