MILAN, Nov 13 (Reuters) - The board of Banca Monte dei Paschi di Siena will meet on Monday to set the terms for a bond-to-equity conversion that is part of the lender's capital boosting plans, a source familiar with the matter said on Sunday.

Italy's third-biggest bank is planning to lay off a tenth of its staff, shut branches and sell assets to win investor backing for a 5 billion euros ($5.4 billion) cash call, its third recapitalisation in as many years.

To help limit the size of the share sale it is studying a voluntary conversion of its subordinated debt.

"The (conversion) operation will kick off after the shareholder meeting... and there will obviously be a premium offered to market price," the source said.

The conversion plan will also include the Fresh hybrid instrument used to partly finance the costly acquisition of rival Antonveneta in 2007, the source said.

Senior debt is not included in the plan.

The bank - assisted by JP Morgan and Mediobanca - is due to hold an extraordinary shareholder meeting on Nov. 24 to approve the turnaround plan that also includes the sale of some 28 billion euros in bad loans at below book value.

To underpin the cash call, management at the 544-year old lender has been on road shows to drum up support from potential anchor investors.

Qatar's sovereign wealth fund has expressed a preliminary interest, sources said earlier this month.

"Next week the road show will continue with a video call with U.S. and Asian investors," the source said.

On Sunday, Il Sole 24 Ore said the bank was reaching out to Asian investors, especially Singapore wealth fund Temesek.

According to the source, the board meeting on Monday will also take a decision on the sale of the lender's non-performing loans servicing platform known as Juliet.

Last week Italian Information Solutions company Cerved said it had presented an offer for the platform.

($1 = 0.9217 euros) (Reporting by Paola Arosio, writing by Stephen Jewkes; Editing by Alexandra Hudson)