A capillary-induced phase separation (CIPS) can arise in a polymer solution enclosed between two walls, provided the solution is close to phase separation. Here the CIPS phenomenon is investigated in binary and quasi-binary polymer solutions by a mean-field lattice theory. A quasi-binary polymer solution represents a binary polymer solution with a polydisperse polymer. The CIPS involves a new phase between the two walls with a different solute composition than the surrounding solution. The molecular length of the polymer, the interaction between the polymer and the walls, and the separation between the two walls are factors that all influence the CIPS. A polydisperse polymer, as in the quasi-binary polymer solutions, will give a slightly increased tendency for CIPS at short distances between the walls, while the effect decays at larger separations.