Context. Observations suggest that most long duration gamma-ray bursts (GRBs) are connected with broad-line supernovae Ib/c, (SNe-Ibc). The presence of GRB-SNe is revealed by rebrightenings emerging from the optical GRB afterglow 10–15 days, in the rest-frame of the source, after the prompt GRB emission. Aims. Fermi/GBM has a field of view (FoV) about 6.5 times larger than the FoV of Swift, therefore we expect that a number of GRB-SN connections have been missed because of lack of optical and X-ray instruments on board of Fermi, which are essential for revealing SNe associated with GRBs. This has motivated our search in the Fermi catalog for possible GRB-SN events. Methods. The search for possible GRB-SN associations follows two requirements: (1) SNe should fall inside the Fermi/GBM error box of the considered long GRB, and (2) this GRB should occur within 20 days before the SN event. Results. We have found five cases within z< 0.2 fulfilling the above reported requirements. One of them, GRB 130702A-SN 2013dx, was already known to have a GRB-SN association. We have analyzed the remaining four cases and we have concluded that three of them are, very likely, just random coincidences due to the Fermi/GBM large error box associated with each GRB detection. We found one GRB possibly associated with a SN 1998bw-like source, GRB 120121B/SN 2012ba. Conclusions. The very low redshift of GRB 120121B/SN 2012ba (z = 0.017) implies a low isotropic energy of this burst (Eiso = 1.39 × 1048) erg. We then compute the rate of Fermi low-luminosity GRBs connected with SNe to be ρ0,b ≤ 770 Gpc-3 yr-1. We estimate that Fermi/GBM could detect 1–4 GRBs-SNe within z ≤ 0.2 in the next 4 years.