For this to be possible there are a few things required. Firstly your device needs to have 'monitor' mode support. This is because all network interfaces will ignore traffic not intended for them unless otherwise told to do so, this is not needed for normal operation so not all devices support it.
Secondly you will need a rooted device as shell commands need to be executed with root (administrative) access. If your phone is not unlocked and rooted this will also not be possible for you.
Thirdly, you will require either a kernel that supports monitoring and snooping on your wireless chipset, or a kernel module that will add this support. This is a technical detail that I will not go in to here, but Googling it will help you.
Last you require a toolset such as airmon (Like you've used on your PC) for Android, there is one on the Play Store here: AirMon.
A word of warning, expect to be on your own out there. Finding a developer that writes these kind of kernel modules or hacking/penetration related tools is usually not open to hand-holding. You will have to Google and help yourself for the most part, or ask more questions on StackOverflow of course.
So the Cliff Note, TL;DR. It's possible, very possible. But you might not be able to do it on your device.
Also, I'm not aware of your skill-set but the hours and skills spent getting this sort of thing to work on a PC let alone a phone are long and vast, so it's best to use the tools others have provided, developing them yourself is going to have a steep learning curve.