Bluetooth for battery operated devices. Reduce power consumption in listen mode.

For my project I made an android phone app that can monitor system status by connecting to arduino via bluetooth. It is working fine but consumes around 35mA in listen mode and 7 mA when connected. I have tried HC-05 and HC-06. I cant afford more than 1mA in listen mode. Is there any trick to save power? I can not touch the device to manually press 'connect' button neither I can disconnect bluetooth module when not in use. What are my other options to save power. How does sleep mode will perform? Does BLE modules are efficient in listen mode?

parthk:
I have tried HC-05 and HC-06.

It might be time to check out the HM-10.

I would refer you to Nick Gammons excellent article on power saving techniques.

Which Arduino board are you using? Each board has a certain amount of power that it uses as a Minimum due to the onboard Hardware which isn't particularly power efficient. A Special built bare-bone is always built but may exceed skills/time etc. I have become particularly fond of the Sparkfun Pro Mini because the newer Versions of this board have a single solder Bridge that can be removed making the Thing nearly a "bare-bone".

@JaBa. Yes I have used those techniques in past and received good results but my problem is with Bluetooth side. Its consuming ton of power when nothing is connected to it. And most of the time there wont be anything connected to it.