The UGTT union mediated the meeting between the ruling Ennahda party and the opposition in Tunis, The Daily Star (Lebanon) reported.
UGTT said the meeting was aimed at creating "a set of decisions to accelerate the adoption of the constitution."
Local media reported four people -- veteran politicians Mohamed Ennaceur and Ahmed Mestiri, and prominent economists Mustapha Kamel Nabli and Jalloul Ayed -- are vying for the position of prime minister.
Ennahda and the opposition said they would name the successor to Ali Larayedh Saturday.
After the prime minister is named, he will have two weeks to form a government of independents to prepare for upcoming elections.