Yet if Italy nominates someone other then Bini Smaghi it risks jeopardizing the chances of Draghi to become president, as several euro zone countries have made clear they will not accept having two Italians on the ECB's board.
If Italy sought to remove Bini Smaghi from the ECB against his will before his mandate ends in 2013, the ECB would mount a legal challenge against what would be seen as an attack on the bank's independence, one ECB source said.
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The ECB has already received an internal legal opinion on the situation, he added.
According to this opinion if Bini Smaghi left for a position below the one he has now it would be clear he had been put under pressure and that would violate the independence of the governing council.
"Bini Smaghi is in a very strong position, his seat on the board is secure unless he is made an offer he can't refuse," another senior source said. "If someone wants to force him out that will not work."
Three sources told Reuters they expected Bini Smaghi would only leave the ECB board if he were offered Draghi's job as Bank of Italy governor, and he would have the ECB's backing.
In this way he would maintain a vote on the ECB's governing council, would remain within the European System of Central Banks (ESCB) and the ECB's independence would be preserved.
And if Bini Smaghi does not leave the ECB board, other countries, including France, have made it clear that they would re-consider their backing for Draghi to take over as president.
Grilli, in particular could cause a problem because he is considered to have the strong backing of Economy Minister Giulio Tremonti, whose reputation as the guarantor of Italian public finances makes him indispensable to the government.
If Berlusconi has not resolved the issue before a European Union summit on June 24 "he will face a lot of pressure" from his fellow leaders, one ECB source said.
The only justification for curtailing an ECB board member's mandate would be if he were offered a similar and equally senior position, a senior European Union source told Reuters.
However, another euro zone central bank source was less sympathetic to Bini Smaghi, saying this principle was not written down, and Bini Smaghi would risk angering the Italian and other governments if Berlusconi did not offer him the BOI job and he refused to resign.
(Reporting by Marc Jones, Gavin Jones, Paul Taylor, Francesca Landini; Writing by Gavin Jones; Editing by Toby Chopra)