We compute the µ → e conversion in the type-I seesaw model, as a function of the right-handed neutrino mixings and masses. The results are compared with previous computations in the literature. We determine the definite predictions resulting for the ratios between the µ → e conversion rate for a given nucleus and the rate of two other processes which also involve a µ − e flavour transition: µ → eγ and µ → eee. For a quasi-degenerate mass spectrum of right-handed neutrino masses -which is the most natural scenario leading to observable rates-those ratios depend only on the seesaw mass scale, offering a quite interesting testing ground. In the case of sterile neutrinos heavier than the electroweak scale, these ratios vanish typically for a mass scale of order a few TeV. Furthermore, the analysis performed here is also valid down to very light masses. It turns out that planned µ → e conversion experiments would be sensitive to masses as low as 2 MeV. Taking into account other experimental constraints, we show that future µ → e conversion experiments will be fully relevant to detect or constrain sterile neutrino scenarios in the 2 GeV−1000 TeV mass range.