Public–private partnership (PPP) infrastructure projects have attracted attention over the past few years. In this regard, the selection of private partners is an integral decision to ensure its success. The selection process needs to identify, scrutinize, and pre-qualify potential private partners that sustain the greatest potential in delivering the designated public–private partnership projects. To this end, this research paper proposes an integrated multi-criteria decision-making (MCDM) model for the purpose of selection of the best private partners in PPP projects. The developed model (HYBD_MCDM) is conceptualized based on two tiers of multi-criteria decision making. In the first tier, the fuzzy analytical network process (FANP) is exploited to scrutinize the relative importance of the priorities of the selection criteria of private partners. In this respect, the PPP selection criteria are categorized as safety, environmental, technical, financial, political policy, and managerial. In the second tier, a set of seven multi-criteria decision-making (MCDM) algorithms is leveraged to determine the best private partners to deliver PPP projects. These algorithms comprise the combined compromise solution (CoCoSo), simple weighted sum product (WISP), measurement alternatives and ranking according to compromise solution (MARCOS), combinative distance-based assessment (CODAS), weighted aggregate sum product assessment (WASPAS), technique for order of preference by similarity to ideal solution (TOPSIS), and FANP. Thereafter, the Copeland algorithm is deployed to amalgamate the obtained rankings from the seven MCDM algorithms. Four real-world case studies are analyzed to test the implementation and applicability of the developed integrated model. The results indicate that varying levels of importance were exhibited among the managerial, political, and safety and environmental criteria based on the nature of the infrastructure projects. Additionally, the financial and technical criteria were appended as the most important criteria across the different infrastructure projects. It can be argued that the developed model can guide executives of governments to appraise their partner’s ability to achieve their strategic objectives. It also sheds light on prospective private partners’ strengths, weaknesses, and capacities in an attempt to neutralize threats and exploit opportunities offered by today’s construction business market.