High-resolution (R = 143,000), high signal-to-noise ratio (S/N = 700-1100) Gemini-S bench-mounted High-Resolution Optical Spectrograph spectra have been analyzed in a search for Li-6 in five stars which host extrasolar planets. The presence of detectable amounts of Li-6 in these mature, solar-type stars is a good monitor of accretion of planetary disk material, or solid bodies themselves, into the outer layers of the parent stars. Detailed profile fitting of the Li I resonance doublet at lambda 6707.8 angstrom reveals no detectable amounts of Li-6 in any star in our sample. The list of stars analyzed includes HD 82943 for which Li-6 has been previously detected at the level of Li-6/Li-7 = 0.05 +/- 0.02. The typical limits in the derived isotopic fraction are Li-6/Li-7 <= 0.00-0.02. These upper limits constrain the amount of accreted material to less than similar to 0.02-0.5 Jovian masses. The presence of detectable amounts of 6Li would manifest itself as a red asymmetry in the Li I line profile and the derived upper limits on such asymmetries are discussed in light of three-dimensional hydrodynamic model atmospheres, where convective motions also give rise to slight red asymmetries in line profiles.