Coronal lines are forbidden emission lines with a ionisation potential χ ≳ 100 eV. They are linked to energetic phenomena triggered by active galactic nuclei (AGNs) in the circumnuclear medium. We present the first high-angular-resolution integral-field analysis of the [Fe VII] λ6087 coronal line in a sample of four nearby low-inclination Seyfert galaxies of which three are of Type 1 and one of Type 2. The data were obtained with the adaptive-optics-assisted mode of MUSE, and have angular resolutions of 0.″06 ‑ 0.″18, allowing us to probe regions down to a few tens of parsecs in size. In three of the objects, we find a resolved coronal emission in a relatively compact configuration (∼200 pc in radius in the most extended case). The coronal emission is smooth and symmetric with respect to the centre of the galaxy, except for one object where an off-nucleus clump of emission is detected. Through the use of spectroastrometry we find that the [Fe VII] λ6087 outflow of the Type 2 AGN host has a redshifted and a blueshifted component whose centroids are separated by ∼20 pc. We interpret this as evidence that some of the coronal emission comes from the inner part of a biconic outflow, also seen in low-ionisation lines such as [O III] λ5007. Similar [Fe VII] λ6087 properties are found in two of the Type 1 AGN hosts, but with a much smaller separation between the centroids of the lobes of the outflow (< 7 pc). This small projected separation compared to that in the Type 2 host could be due to the foreshortening of the axis of the bicone in Type 1 objects. We also studied the spectrum of the unresolved nuclear source and found that in three out of four galaxies a fraction of at least ∼60% of the [Fe VII] λ6087 emission has kinematics similar to those of [O III] λ5007. We conclude that part of the coronal emission within the inner few tens of parsecs is co-spatial and shares kinematics with the outflows as traced by lower-ionisation lines. ⋆ Based on observations made at the European Southern Observatory using the Very Large Telescope under programmes 60.A-9100(K), 60.A-9493(A), 0103.B-0349(A), 0103.B-0908(A), and 0106.B-0360(A).