The production of φ-mesons in proton-proton collisions is investigated within a relativistic meson-exchange model of hadronic interactions. The experimental prerequisites for extracting the N N φ coupling strength from this reaction are discussed. In the absence of a sufficient set of data, which would enable an accurate determination of the N N φ coupling strength, we perform a combined analysis, based on some reasonable assumptions, of the existing data for both ω-and φ-meson production. We find that the recent data from the DISTO collaboration on the angular distribution of the φ meson indicate that the N N φ coupling constant is small. The analysis yields values for g N N φ that are compatible with the OZI rule.