Nanoelectromechanical systems(1,2) based on cantilevers have consistently set records for sensitivity in measurements of displacement(3), force(4) and mass(3,5,6) over the past decade. Continued progress will require the integration of efficient transduction on a chip so that nanoelectromechanical systems may be operated at higher speeds and sensitivities. Conventional electrical schemes have limited bandwidth(7,8), and although optical methods(9,10) are fast, they are subject to the diffraction limit. Here, we demonstrate the integration of nanocantilevers on a silicon photonic platform with a non-interferometric transduction scheme that avoids the diffraction limit by making use of near-field effects in optomechanical interactions(11). The use of a non-interferometric method means that a coherent light source is not required, making the monolithic integration of optomechanical systems with on-chip light sources feasible. We further demonstrate optomechanical multiplexing of an array of ten nanocantilevers with a displacement sensitivity of 40 fm Hz(-1/2).