Well, it is totally possible and here is how to do it.
There are 4 basic things that need to be done:
convert the analog signal into pulse width modulation (PWM)
read the PWM on any GPIO
read the PWM duty cycle on the ESP8266
calibrate the PWM to analog level response
I am using NodeMCU Lua API.
For more details on the project and description visit http://www.horaciobouzas.com