Detrending of variables

Hi, to stationarize the model, which endogenous variables need to be detrend?
Does the monetary base and its components need to be detrend?

Are you talking about empirical data? In that case, everything that grows over time needs to be stationarized. That applies to the monetary base as well.

My argument is theoretical and related to model, not data. Do monetary variables detrend with the price index and gross inflation or do they need to be detrend with a growth rate as variables like consumption?

The answer to that question depends on the particular conduct of monetary policy. But empirically, the ratio of the money stock to nominal GDP is roughly constant. So it grows with prices and real output growth.