Thanks guys for your suggestions. I finally managed to make it work but without the ADS. I'm not giving up with the ADS but I needed to have something working. I'm using the D1 mini and the pot is connected to the analog. I have 120uA during the deep sleep which is reasonable at the moment.
The only problem is the repeatability. I blocked the pot against a piece of wood but the signal is not exactly the same each time. The maximum variation is +/- ~0.2 mm (out of 50 mm) which is not acceptable (compared to another pot / configuration) I was using before. I'm not sure if it's due to the stability of the voltage after the deepsleep even if I have a 2sec delay after it wakes up, or the cheap pot that I'm using. I will receive more accurate pot this week and will try again with them.
I will let you know. Thanks again