Coalition members have carefully avoided naming the ministers – Economics Minister Mihkel Parnoja and Transportation and Communications Minister Toivo Jurgenson – in recent speeches.
Estonian President Lennart Meri also suggested replacing some of the unpopular ministers with more competent ones in order to improve the prospects of the coalition in the next parliamentary elections, the daily Eesti Paeveleht reported.
Prime Minister Mart Laar admitted the need for change, but said it could not happen before new regulations concerning the replacement of ministers are approved by the coalition's council, he said in an interview to Eesti Raadio.
The chairman of the coalition council Andres Tarand prepared the reshuffle plan this week and the coalition is supposed to express an opinion about the changes within two weeks.
"It's about the image of the government," said Laar.
Tarand believes that the ministers should not be replaced until their guilt has been proven. He said that the ministers have done what the Parliament or government has told them to do.
Former Prime Minister Mart Siimann, who currently heads the Coalition Party faction, believes the prime minister should step down instead of blaming the ministers whom he picked.
He said Laar's resignation would also relieve political tensions and save the coalition's image for the remaining two years of its scheduled term.
The opposition is also planning a no-confidence vote against Laar in the first week of April on the basis of the high unemployment level and confusion over the railway privatization.
The vice chairman of the Centrist Party, Peeter Kreitzberg, told Eesti Paeveleht that the coalition's image would not improve unless at least half of the ministers and the prime minister stepped down.
Unlike Siimann, the president praised the skills of the prime minister in keeping the ruling coalition together and securing the development of the state.
Members of the Reform Party from Tartu declared on March 30 that the problem ministers should step down regardless of whether they are guilty or not, because people have lost faith in them.
But Andrus Ansip, the mayor of Tartu, said that only the ministers who failed to do their work properly should step down.
Since Jurgenson represents the Pro Patria Union and Parnoja the Moderates, the third member leaving office could come from the Reform Party and, according to BNS, it might be Regional Affairs Minister Toivo Asmer.
"How the mechanism of the replacement of ministers will work in the future depends on the coalition council's decision," said Laar.
In the past ministers were replaced by MPs from their own parties.
Parnoja is not willing to step down of his own accord until he is asked to resign by his party.
"If I resigned now of my own accord I'd give the impression that the largely unfounded accusations directed towards me are true," he said at a March 27 news conference.
The Pro Patria Union party has suggested replacing the two unpopular ministers with 31-year-old Kersti Kaljulaid, who works as an economics adviser to the prime minister. She joined the party three weeks ago.
In spite of the scandals, support for the opposition has never exceeded the combined popularity of the governing coalition.