Clay liners are widely used as porous membrane barriers to control solute transport and to prevent the leakage of leachate both in horizontal and vertical flow scenarios, such as the isolated base and ramps of sanitary landfills. Despite the primary importance of saturated hydraulic conductivity in a reliable simulation of fluid flow through clay barriers, there is no model to predict hydraulic conductivity of clayey soils permeated with saline aqueous solutions because most of the current models were developed for pure water. Therefore, the main motivation behind this study is to derive semi-empirical models for simulating the hydraulic conductivity of clayey soils in the presence of arbitrary solute concentrations in addition to deionized water. In order to achieve this goal, a relatively comprehensive dataset of 842 measured hydraulic conductivities was retrieved from the experimental literature, where almost 44% of them are related to certain solute concentrations. Afterwards, two modelling approaches were introduced; the first one is a modified form of Mbonimpa et al.'s (2002) model, in which the constants are adjusted to take into consideration the variations in liquid limit due to a change in solute concentration. A modification term was added to the model for the sake of accuracy. In the second approach, a new form of solute concentration-dependent hydraulic conductivity function was proposed, where special attention was given to void ratio and adaptive liquid limit as effective parameters. The results revealed that hydraulic conductivity predictions could be erroneous if the influence of solute concentrations in permeating fluid is ignored. An error analysis was conducted to examine the models' applicability and deviations. A blind independent set of data, including 132 data points, was also used to verify models. On the other hand, both newly proposed models could predict the hydraulic conductivity for a variety of soils, salt species, and concentrations well. Therefore, the proposed modelling approaches are somehow unique by considering the salinity of the pore fluid in addition to deionized water. More importantly, both models are comprised of easy-to-measure parameters with clear physics-based implications.