In this work we show that the electrical conductivity and thermoelectric power of random networks of carbon nanotube (CNT) films can be tuned by means of a layer-by-layer polymer coating technique of the individual nanotubes. Using this approach, nanotubes dispersed in water are coated before the formation of the film, achieving a control of the transport properties independent of the substrate. Below a certain temperature the conductivity departs from the ohmic behavior and enters a tunneling regime with an energy barrier for electron transport determined by the width of the polymer layer. The excellent control over the conductivity and the possibility of using the polymer coating as a gate dielectric material could be an important step for the development of an easy and scalable approach for the fabrication of CNT-based thin film transistors.