A process for the manufacture of a precursor gel of a support for a catalyst, including steps for, in a first stage, mixing an alcohol, water, a silicon alkoxide and an acid in amounts such that the water/silicon molar ratio is from 2 to 50, adding an acidic solution of an aluminium compound and/or a solution of a source of phosphate ions, in a second stage, and, in a third stage, adding a gelling agent to the hydrolysis medium thus obtained, the first stage being carried out at acid pH and the temperature during the addition of water, acid, silicon, alkoxide and alcohol being less than or equal to 30.degree. C. and, the first stage also including a maturing of the hydrolysis medium thus obtained at a temperature at least equal to 20.degree. C. and lower than the boiling temperature of the medium, so as to substitute at least part of the alkoxy groups of the silicon alkoxide by hydroxyl groups, without producing precipitation or gelling of silica.