N-vinylpyrrolidone-co-allylamine copolymers (VP-co-AA) containing iminodiacetic (IDA) chelation units were prepared in the range of molecular masses of the copolymers from 9000 to 30,000 Da depending on polymerization conditions. Non-radioactive organometallic species Re(CO)3+ were introduced into polymeric carriers under mild conditions; the prepared metal–polymeric complexes were characterized by IR, NMR, ESI-MS and HPLC. IR spectra data confirmed the coordination of M(CO)3+ moiety to the polymeric backbone via IDA chelation unit (appearance of characteristic fac-M(CO)3+ vibrations (2005, 1890 cm−1), as well as the appearance of group of signals in 1H NMR spectra, corresponding to those inequivalent to methylene protons CH2COO (dd, 4.2 ppm), coordinated to metal ions. The optimal conditions for labeling the PVP-co-AA-IDA copolymers with radioactive 99mTc(CO)3+ species were determined. The radiochemical yields reached 97%. The obtained radiolabeled polymers were stable in blood serum for 3 h. In vivo distribution experiments in intact animals showed the high primary accumulation of technetium-99m MPC (MM = 15,000 Da) in blood with subsequent excretion via the urinary tract.