In this paper, we investigate the possibility of significant production of thermal bremsstrahlung radiation at radio continuum frequencies that could be linked to some Galactic supernova remnants (SNRs). The main targets for this investigation are SNRs expanding in high density environments. There are several indicators of radio thermal bremsstrahlung radiation from SNRs, such as a flattening at higher frequencies and thermal absorption at lower frequencies intrinsic to an SNR. In this work we discuss the radio continuum properties of 3 SNRs that are the best candidates for testing our hypothesis of significant thermal emission. In the case of SNRs IC443 and 3C391, thermal absorption has been previously detected. For IC443, the contribution of thermal emission at 1 GHz, from our model fit is 3-57%. It is similar to the estimate obtained from the thermal absorption properties (10-40% at 1 GHz). In the case of the 3C391 the conclusions are not so clear. The results from our model fit (thermal emission contribution of 10-25% at 1 GHz) and results obtained from the low frequency absorption (thermal contribution of 0.15-7% at 1 GHz) do not overlap. For the SNR 3C396 we suggest that if previously detected thermal absorption could be intrinsic to the SNR then the thermal emission (<47% at 1 GHz from our model fit) could be significant enough to shape the radio continuum spectrum at high frequencies. Polarization observations for these SNRs can constrain the strength of a thermal component. Reliable observations at low frequencies (<100 MHz) are needed as well as more data at high radio frequencies (>1 GHz), in order to make stronger conclusions about the existence of radio thermally active SNRs.