For the Roman Church, each Bishop of a diocese is expecet to regularly submit names of priest that he considers good men to be ordained as bishops. How and what qualifications that bishop would use are up to him.
A Bishop could only nominate Monsignors if he so wanted, or he could choose other criteria.
Those names are submitted to the Papal Nuncio, the Pope’s Official represtative to a country.
The Papal Nuncio with compile additional information about the men nominated and forward that information, potentially along with his recommendations, to the Holy Father.
The Holy Father, often with further consultation, will name bishops as he sees fit.
Needless to say, the Holy Father is under no obligation to use anyone’s recommendations, but operates using the supreme authority of his Office.
There is a seperate process for the Eastern Churches.