The presence of possible blends in the spectral region of the Li resonance line at 6708 Å in solar-type metal-rich stars is investigated using high resolution and high signal-to-noise spectroscopic observations. Our analysis does not confirm the identification of a weak absorption feature at 6708.025 Å with the low excitation Ti I line proposed by Reddy et al. (2002). Our spectrum synthesis suggests that the unidentified absorption is most probably produced by a high excitation Si I line originally proposed by Müller et al. (1975). Reanalysis of the 6Li/7Li isotopic ratio in HD 82943 was performed by taking the Si I line into account and using new VLT/UVES spectra of HD 82943 with a signal-to-noise ratio close to 1000. We confirm the presence of 6Li in the star's atmosphere while the updated value for the isotopic ratio is f(6Li) = 0.05+/-0.02. Based on observations collected at the La Silla Observatory, ESO (Chile), with the FEROS spectrograph at the 1.52-m ESO telescope, with the VLT/UT2 Kueyen telescope (Paranal Observatory, ESO, Chile) using the UVES spectrograph (Observing run 67.C-0206, in service mode), with the TNG and William Herschel Telescopes, both operated at the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.