MILAN, Aug 9 (Reuters) - DBRS Morningstar said on Monday it had downgraded Monte dei Paschi's (MPS) subordinated debt, citing increased risks that holders of the state-owned Italian bank's junior debt may have to bear losses as part of its re-privatisation.

The credit rating agency said in a note it had cut the rating on the bonds to 'CCC' from 'B(low)'. The trend is stable.

The action "reflects the increased risk of burden-sharing on these instruments as the Italian government gets closer to finding an exit strategy for its ownership," DBRS said.

Italy's Treasury, which owns 64% of MPS following a 2017 bailout, is in talks to sell the Tuscan bank to healthier rival UniCredit.

Two sources involved in the discussions told Reuters on Friday that the Treasury aimed to seal a possible sale on terms that would spare bondholders from losses. (Reporting by Giulio Piovaccari; Editing by Valentina Za and Alexander Smith)