We analyse the effect of foregrounds on the observed alignment of the cosmic microwave background radiation (CMBR) quadrupole and octopole. The alignment between these multipoles is studied by using a symmetry-based approach which assigns a principal eigenvector (PEV) or an axis with each multipole. We determine the alignment between these multipoles and its significance using the internal linear combination (ILC) 5- and 7-yr maps. We also use the maps obtained by applying the internal power spectrum estimation (IPSE) procedure on the corresponding Wilkinson Microwave Anisotropy Probe data sets to assess its significance. The effect of foreground cleaning is studied in detail within the framework of the IPSE method both analytically and numerically. By using simulated CMBR data, including foregrounds and detector noise, we study how the PEVs of the simulated pure CMB maps differ from those of the corresponding clean maps. We find that, in general, the shift in the PEVs is relatively small and in random directions. Because of the random nature of the shift we conclude that the residual foregrounds can only lead to misalignment rather than cause alignment of multipoles. We also directly estimate the significance of the observed alignment by using simulated clean maps. We find that the results in this case are identical to those obtained by simple analytic estimates or by using simulated pure CMB maps.