Recent theoretical and simulation studies suggest an unexpected shift in the solubility of n-alkanes in near-critical water, which would indicate that longer n-alkane molecules are more soluble than shorter ones. This trend is contrary to what one finds at ambient conditions, where longer alkanes generally have a lower aqueous solubility. The latter is usually interpreted as a consequence of the greater hydrophobicity of longer chains. There is also evidence that the reversal in the solubility close to the critical region may disappear at temperatures well above the critical point. We investigate these phenomena using a simplified version of the statistical associating fluid theory (SAFT) in which molecules are modeled as associating chains of hard-sphere segments with van der Waals mean-field dispersion interactions. Within the SAFT approach it is possible to take into account explicitly the extensive hydrogen bonding present in water and in aqueous solutions as well as the chainlike nature of the n-alkane molecules. Both of these features cause anisotropies in the molecular interactions and are responsible for the large nonideality of these systems. The SAFT-HS calculations are compared with available molecular dynamics simulations in an effort to further explore and understand this unexpected behavior. While the SAFT and simulation results agree concerning the reversal and rereversal seen in the Gibbs free energy of solvation (and equivalently the Henry's law constant), the SAFT results suggest that this is not related to changes in alkane solubility, since according to the SAFT calculations the alkanes and water are miscible at the temperature and pressure at which reversal and rereversal of the Gibbs free energy take place.