We present the results of the ongoing XMM-Newton survey of M31. 17 X-ray sources detected in the survey have bright radio counterparts, and 15 X-ray sources coincide with SNR candidates from optical and radio surveys. 15 out of 17 sources with radio counterparts, not SNR candidates, have spectral properties similar to that observed for background radio galaxies/quasars or Crab-like supernova remnants located in M31. The remaining two sources, XMMU J004046.8+405525 and XMMU J004249.1+412407, have soft X-ray spectra, and are associated with spatially resolved H-alpha emission regions, which makes them two new SNR candidates in M31. The observed absorbed X-ray luminosities of SNR candidates in our sample range from 1e35 to 5e36 ergs/s, assuming the distance of 760 kpc. Most of the SNR candidates detected in our survey have soft X-ray spectra. The spectra of the brightest sources show presence of emission lines and can be fit by thermal plasma models with kT~0.1-0.4 keV. The results of spectral fitting of SNR candidates suggest that most of them should be located in a relatively low density regions. We show that X-ray color-color diagrams can be useful tool for distinguishing between intrinsically hard background radio sources and Crab-like SNR and thermal SNR in M31 with soft spectra.