Quantum computers require interfaces with classical electronics for efficient qubit control, measurement and fast data processing. Fabricating the qubit and the classical control layer using the same technology is appealing because it will facilitate the integration process, improving feedback speeds and offer potential solutions to wiring and layout challenges. Integrating classical and quantum devices monolithically, using complementary metal-oxide-transistor (CMOS) processes, enables the processor to profit from the most mature industrial technology for the fabrication of large scale circuits. Here we demonstrate the integration of a single-electron charge storage CMOS quantum dot with a CMOS transistor for control of the readout via gate-based dispersive sensing using a lumped element $LC$ resonator. The control field-effect transistor (FET) and quantum dot are fabricated on the same chip using fully-depleted silicon-on-insulator technology. We obtain a charge sensitivity of $delta q=165, mu e mathrm{Hz}^{-1/2}$ when the quantum dot readout is enabled by the control FET. Additionally, we observe a single-electron retention time of the order of a second when storing a single-electron charge on the quantum dot at milli-Kelvin temperatures. These results demonstrate first steps towards time-based multiplexing of gate-based dispersive qubit readout in CMOS technology opening the path for the development of an all-silicon quantum-classical processor.