Šalaševičiūtė, a social democrat, resigned earlier this month, following criticism from President Dalia Grybauskaitė, Prime Minister Algirdas Butkevičius and members of her party.
She had admitted on live radio about having offered a small informal payment to a doctor a decade ago. She was also been questioned in a corruption investigation concerning a hospital in Šiauliai.
Prime Minister Butkevičius said on Thursday he had to candidates in mind for the post, but would not reveal them.
The new healthcare minister will be proposed on February 29, after the Social Democratic Party's presidium convenes for a meeting to decide on the candidate, he said.