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This data article describes the connected pore cluster data from segmented nano-images of rocks related to a geothermal system. The collected samples include two (2) vesicle-amygdaloidal basalt (host rock) and four (4) horizons collected from a siliceous sinter mound (rock precipitated from hot waters). All the samples have undergone computed tomography scanning using a SkyScan 2211 multiscale X-ray nano-CT system (Bruker®), and the slices were analyzed using the Digital Rock Physics (DRP) approach. Pore volume and fluid permeability in the three directions were calculated with scripts of Python (v.3.9) and the visualizations of the 3D models were run with Paraview (v.5.10) software. The petrophysical properties, diagrams, and figures were produced by stacking the 2D projections (8-bit grayscale *.png images format) from the scanning. Raw data (images) were deposited in a repository, which has granted a persistent identifier (Mendeley Data: https://data.mendeley.com/datasets/srpxhpd37p/2). This article provides a study case to handle the data that test the interconnectivity and ability to transport fluids and/or exogenous matter carried during high-flow events in rocks outcropping at the surface level of a geothermal system., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 The Author(s).)