Aims. The clusters Abell 2061 and Abell 2067 in the Corona Borealis supercluster have been studied at different radio frequencies and are both known to host diffuse radio emission. The aim of this work is to investigate the radio emission between them, whose presence is suggested by low-resolution observations. Methods. We analysed deep LOw Frequency ARray (LOFAR) High Band Antenna (HBA) observations at 144 MHz to follow up on the possible inter-cluster filament suggested by previous 1.4 GHz observations. We investigated the radial profiles and the point-to-point surface-brightness correlation of the emission in Abell 2061 with radio and X-ray observations to describe the nature of the diffuse emission. Results. We report the detection of diffuse radio emission on an 800 kpc scale, which is more extended than previously known, reaching beyond the radio halo in Abell 2061 towards Abell 2067 and over the separation outside the two clusters R500 radii. We confirm the presence of a radio halo in A2061, while we do not find evidence of diffuse emission in Abell 2067. The surface-brightness profile from the centre of A2061 shows an excess of emission with respect to the azimuthally averaged radio halo profile and X-ray background. We explored three different dynamical scenarios to explain the nature of the diffuse emission. Additionally, we analysed a trail of emission of ∼760 kpc between the radio halo and radio relic in Abell 2061. Conclusions. This dynamically interacting, pre-merger system closely resembles the two other cluster pairs where radio bridges connecting the radio halos on Megaparsecs scales have been detected. The diffuse emission extends beyond each cluster R500 radius, but in this unique case the absence of the radio halo in Abell 2067 is likely the reason for the observed ‘gap’ between the two systems. However, the point-to-point correlation results are challenging to explain. The classification of the emission remains unclear, and detailed spectral analysis and further X-ray observations are required to understand the origin of the diffuse emission.