Massive star clusters (MSCs) have recently received renewed attention as possible cosmic ray (CR) factories. In fact, the conversion of few % of the cluster kinetic energy into accelerated particles can easily account for the $\gamma$-ray emission observed in coincidence with some MSCs, in a scenario where gamma-rays would result from pions produced in collisions between the relativistic hadrons and the ambient gas. In addition, the $\gamma$-ray spatial profile suggests that CRs are continuously produced during a period compatible with the typical age of a MSC. Cygnus OB2 is one of the most massive star clusters in the Milky Way, located near the Cygnus X star-forming complex. Fermi-LAT observations of the region revealed an extended gamma-ray emission (Cygnus Cocoon) possibly coming from CRs accelerated by Cygnus OB2. Recent studies claim that this extended emission is compatible with a CR distribution of freshly accelerated escaping particles. In this work, we compare the observed $\gamma$-ray emission and its radial profile with the prediction of a theoretical model where particles are accelerated at the termination shock of the cluster wind. In particular, we study the impact that different distribution of gas around the cluster have in shaping the Cocoon morphology. While the total $\gamma$-ray emission is very well reproduced, implying a maximum energy of accelerated protons of $\sim 100$ TeV, the predicted radial shape is almost flat, compatible with HAWC data but not with Fermi-LAT ones.