Fibre materials are widely used as insulation materials in both clothing and the building industry. The transport of heat and air through fibre insulation materials are accountable for both the energy need for indoor space conditioning and the indoor environment quality inside buildings. A better understanding of the thermodynamics of those materials can enable higher quality products for improved energy efficiency. By using fast gas permeability measurements and more time-consuming guarded hot plate measurements, this study investigates the link between thermal conductivity and gas permeability for Rockwool, Kevlar and polyester fibres, at different compaction levels. Correlations between gas permeability and thermal conductivity at different total volumes of solid are presented. The experimental results show that the gas permeability and thermal conductivity exhibited a change in their evolution trend, due to compaction, in the same zone of the total volume of solid for all materials. The presence of this transition zone enables to establish a link between the measurement of gas permeability and thermal conductivity. This correlation can be employed to perform rapid thermal conductivity assessment of fibrous material, which can be cost-effective for fibre manufacturers or building contractors, but also quality assessment in the textile industry.