Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair potentials (QGPP) based on the generalized band representation and thereby clarify how the quantum geometry of electrons is transferred to the Cooper pairs they form. QGPP quantifies the deviation of multiband superconductors from an assembly of single-band superconductors and has a direct connection to the quantum-geometric corrections to thermodynamic coefficients. We also discuss their potential ability to emulate exotic pair potentials and engineer intriguing superconducting phenomena including topological superconductivity.