We study the A dependence of the φ meson production cross section in proton nucleus reactios at energies just above threshold, which are accessible in an experimental facility like COSY. This A dependence has two sources: the distortion of the incident proton and the absorption of the φ in its way out of the nucleus. This second process reduces the cross section in about a factor two in heavy nuclei. Thus we show that the A dependence of the cross section contains valuable information on the φ width in the nuclear medium.The study of the properties of vector mesons in a nuclear medium is one of the subjects in hadron physics which receives continuous attention (see for instance Ref.[ 1]). Although originally the ρ meson properties were mostly investigated, nowadays the φ properties have got a lot of interest, because the medium renormalization in this case is more drastic than that of the ρ. Indeed, predictions of an increase of the φ width by a factor five or six [ 2, 3] to ten [ 4], at normal nuclear matter density, have been made using different chiral approaches. Different reactions have been studied or suggested to test experimentally this large width [ 5,6,4,7,8,9].The aim of the present work is to propose a new method to determine the φ width in the nuclear medium [ 10]. The traditional method in the works quoted above (except [ 9]) is to look for a broadening of the φ width reconstructed from the invariant mass of its decay products. Here, instead, we use a different philosophy and we investigate the A dependence of φ production in pA collisions, in a similar way as it was done in [ 9] with the φ photoproduction in nuclei, which is the subject of experimental investigation at Spring8/Osaka [ 11]. The advantage of performing the reaction slightly above threshold is that one can rule out the contribution from coherent φ production which might obscure the interpretation of the experimental results in [ 11]. The present reaction, with its particular kinematics, is amenable of experimental performance at facilities like COSY.In order to implement the relevant nuclear effects in the φ production cross section we will use a model based on many body techniques, successfully applied in the past in many works [ 12,13] to study the interaction of different particles with nuclei. The model assumes a local Fermi sea at each point in the nucleus and provides a very simple and accurate way to account for the Fermi motion of the initial nucleon and the Pauli blocking of the final ones. On the other hand, we have to take into account the distortion of the incoming nucleon and the final φ meson in the their way through the nucleus, which are