The situation was complicated yesterday evening by a decision by the constitutional court to admit nine referendums proposed by civil rights campaigners close to Mr Berlusconi. These could interfere with the timing of an election.
With the political temperature exceptionally high and the lira going into free fall on the financial markets, Mr Scalfaro is under pressure to produce a magic formula that can stabilise the country.
His main obstacle is Mr Berlusconi, who has insisted either on being reinstated or on holding fresh elections immediately. He has resisted considerable pressure to accept an interim administration that would carry out essential economic and institutionalreforms before organising fresh polls in six months or a year.
President Scalfaro has made clear he would prefer the latter option, but may not be sure that any "presidential" government would have the requisite support in parliament.
Yesterday evening there were conflicting signals on the likelihood of him succeeding. Rocco Buttiglione, the head of the Christian Democrat Popular Party and a key player in any parliamentary numbers game, said: "We are heading towards a resolution of the crisis."
The head of a small left-wing party, Michele Selletti, added that Mr Scalfaro "could have a card left up his sleeve" permitting him to set up an interim administration.
Other political sources, however, suggested the president was having trouble persuading any of his prospective candidates to accept the post.
The names most often cited have been Mario Monti, an economist recently appointed a European Commissioner, Lamberto Dini, the outgoing treasury minister, Romano Prodi, a former industrialist with support on both right and left, and Francesco Cossiga, Mr Scalfaro's predecessor.
Mr Monti said last week that he had no intention of abandoning his new job in Brussels.
Mr Dini has come under pressure from Mr Berlusconi not to accept the premiership, while Mr Cossiga has said he would not wish to get involved in governmental politics without the support of the whole political spectrum.
If the president cannot set up an effective interim administration, he has three choices, none of which will please the international community or address the basic instability of the situation: reappointing Mr Berlusconi and leaving him with a minority in parliament, holding elections immediately, or allowing the crisis to drag on longer.