Mr Savisaar's party won most votes
Estonian President Arnold Ruutel has said that either of the two most successful parties in the weekend's general election could potentially form the next government.
Mr Ruutel, whose job it is to nominate a prime minister, said both the left-leaning Centre Party and the conservative Res Publica, who won an equal number of seats, could pursue a dynamic economic policy.
Both parties have ruled out a coalition with each other, but could pull together a majority with the help of smaller parties.
Each has 28 seats in the 101-member parliament.
The new government is expected to take the formerly communist Baltic state into both Nato and the European Union.
Centre Party: 25.4%
Res Publica: 24.6%
Reform Party: 17.76%
People's Union: 13%
Pro Patria: 7.3%
Mr Ruutel told the AFP news agency he would not start official consultations until Wednesday.
The election cements a remarkable comeback for Centre Party leader Mr Savisaar.
He resigned as interior minister in disgrace in 1995 after allegations he had made secret tape recordings of his political rivals.
For the past year, his Centre Party has formed part of the current coalition government under Prime Minister Siim Kallas, of the right-of-centre Reform Party.
The Reform Party limped into third place in the election, with 17.7% of the vote and 19 seats.
Overall, centre-right parties won 60 seats in parliament, with left-oriented parties winning just 41.
Mr Ruutel said the Centre Party and the Reform Party could make an "efficient government" with one or two more parties.
He said Res Publica would be able to seek support from Pro Patria, the People's Union and perhaps the Moderates.
"The only party with which we are not prepared to enter coalition talks is the Centre Party," Res Publica leader Juhan Parts said on Estonian television.
Res Publica campaigned on an anti-crime, anti-corruption platform, and was one the harshest critics of the controversial Mr Savisaar.
However all parties agree on Estonia's pro-Western orientation, its drive to join the EU and Nato.
Estonia - along with Baltic neighbours Latvia and Lithuania - is due to join both organizations in 2004.
Mr Ruutel has two weeks to nominate a prime minister, who would then have to present a cabinet to parliament for approval.