We use computer simulations to investigate how a catalytic reaction in a polymer sol can induce the formation of a polymer gel. To this aim we consider a solution of homopolymers in which freely-diffusing catalysts convert the originally repulsive A monomers into attractive B ones. We find that at low temperatures this reaction transforms the polymer solution into a physical gel that has a remarkably regular mesostructure in the form of a cluster phase, absent in the usual homopolymer gels obtained by a quench in temperature. We investigate how this microstructuring depends on catalyst concentration, temperature, and polymer density and show that the dynamics for its formation can be understood in a semi-quantitative manner using the interaction potentials between the particles as input. The structuring of the copolymers and the AB sequences resulting from the reactions can be discussed in the context of the phase behaviour of correlated random copolymers. The location of the spinodal line as found in our simulations is consistent with analytical predictions. Finally, we show that the observed structuring depends not only on the chemical distribution of the A and B monomers but also on the mode of formation of this distribution.