The main aim of this work is to explore the possibility that cold dark matter (CDM) and early dark energy (EDE) can be described by canonical scalar fields that are coupled at the level of its conservation equations. The formalism covers dynamical aspects at the background and linear perturbation levels for an arbitrary coupling function, followed by an example of it. We emphasize the impact of this model on the Matter Power Spectrum and the Cosmic Microwave Background (CMB) spectra, with or without direct interaction. Our findings indicate that the presence of a scalar field can partially counteract the known effects of the other, opening the possibility to avoid some undesired aspects, such as the increase in $Ω_{m}$ that usually is needed in the case of a purely EDE scalar field scenario, in order to fit the CMB spectra. This opens up the possibility to analyzing whether the interaction can help to ameliorate the cosmological tensions.

14 pages, 10 figures