Rome owns 68% of Monte dei Paschi (MPS) after a 2017 bailout and must cut that stake by mid-2022 at the latest.
Defying growing political and union pressure to delay an exit, the Treasury is pushing ahead with efforts to lure buyers.
Investment banks and law firms have until Nov. 17 to submit their proposals and a decision is expected within a week, the two sources said, speaking on condition of anonymity as the matter is confidential.
Rome has sent out requests for proposals (RFPs) asking advisers to quote a price for their services to support the Treasury in finding a new owner for its stake.
The mandates will last 12 months, the sources said.
Spokesmen for the Treasury and MPS declined to comment.
Italy is seeking ways to address pending legal claims amounting to 10 billion euros (£9 billion) that sources say are the main hurdle to privatising the bank.
MPS is a tough sell in Italy's over-branched banking market, where the pandemic has stoked loan losses and accelerated a switch towards remote banking.
UniCredit is seen as the preferred buyer for MPS given its robust balance sheet, banking sources have said, but any deal would only come after the Treasury acts to remove the legal risks while also injecting fresh capital.
UniCredit boss Jean Pierre Mustier has repeatedly denied any interest in mergers, saying tie-ups only "add staff, branches which UniCredit has been working to reduce".
Rome has set aside 1.5 billion euros to shore up MPS but the bank faces a shortfall of at least 2 billion euros, sources have said.
LEGAL RISKS CONUNDRUM
European Union competition rules make it hard for Rome to provide guarantees against the legal risks associated with MPS after decades of mismanagement and the conviction of former top executives.
The Treasury has lately revisited plans for a possible spin-off of the legal claims to another state-owned entity, three sources with knowledge of the matter said.
Under the proposed scheme, MPS would also transfer the near 1 billion euros in cash set aside against the claims and the Treasury would fill the ensuing capital gap, one of the sources said.
However, under Italian law, MPS could still be held liable for future claims were the recipient company to have insufficient funds to meet its obligations.
If successful, such a scheme would replicate the spin-off of MPS's soured debts in favour of state-owned bad loan manager AMCO, which is due to complete by Dec. 1.
MPS said on Friday it had updated projections on its capital reserves, which the bad loan spin-off is set to reduce by 1.1 billion euros, after increasing provisions against legal risks in the third quarter.
It said the impact of the pandemic and regulatory effects were expected to produce a capital shortfall, adding the Treasury stood ready to support the bank while also seeking a merger to meet commitments made to Brussels.
(Reporting by Pamela Barbaglia in London, Valentina Za in Milan and Giuseppe Fonte in Rome; editing by Barbara Lewis)
By Pamela Barbaglia, Valentina Za and Giuseppe Fonte