The bank needs to raise 5 billion euros ($5.2 billion) by the end of this month to avert being wound down. The Italian government is expected to step in this week to bail it out.
The Tuscan lender, Italy's third biggest bank and the world's oldest, had pinned its hopes on Qatar's sovereign wealth fund investing 1 billion euros in its cash call, but that option is no longer on the table, the sources said.
As a result, the bank entire share sale, which closes at 2 p.m. (1300 GMT) on Thursday, has drawn very little interest from the wider investment community, they added.
The bank declined to comment.