"The selectors need to discuss the issue with the interim committee members of Sri Lanka Cricket. This meeting will take place next week after the current New Year holiday period," Chairman of selectors Duleep Mendis, who took over after the resignation of Aravinda de Silva, told the local media here.
Sangakkara, currently leading the Deccan Chargers in the IPL, resigned from the captaincy in the aftermath of the loss to India in the April 2 World Cup final.
His resignation was followed by that of his deputy Mahela Jayawardene and the chairman of selectors de Silva.
Sangakkara said he was giving Sri Lankan selectors the chance to name a captain who would lead the team in the next World Cup to be held in Australia and New Zealand in 2015.
Tillakaratne Dilshan is tipped to succeed Sangakkara. Dilshan is a year older than Sangakkara at 34.
Sangakkara, it is understood, is willing to captain the Test team in the next two international commitments, the tour of England in May and the visit of Australia in August.