"Shakib will join the squad today and we will assess him further to see if he can play in our next game," selector Habibul Bashar told AFP by phone from Colombo.
Shakib, who normally skippers Bangladesh's short-format side, was ruled out of the tournament after sustaining a finger injury in a one-day international against Sri Lanka in January.
Batsman Mahmudullah Riyad has been acting captain in the tri-series against Sri Lanka and India.
Bangladesh Cricket Board could not immediately confirm if Shakib would return as captain if he was included in the final eleven.
The board's president and several directors were in Sri Lanka and would decide on the captaincy, said BCB spokesman Jalal Yunus.
Bangladesh interim coach Courtney Walsh said any decisions about Shakib taking to the pitch or returning as captain would be made in the interest of the team.
"If he is fit enough to play, then someone of his class and calibre we will have to consider," he told reporters in Colombo.
Sri Lanka coach Chandika Hathurusingha said it would be "a desperate measure" to put Shakib on the field before he was ready.
"If he is really fit, then I think they have advantage, because he is the world's number one all-rounder and we all know that he is a quality player," he told reporters.
Bangladesh will face hosts Sri Lanka in a must-win contest in their final league match of the tournament on Friday.
They have lost to India twice in the tournament but defeated Sri Lanka on their first meeting by completing their record-run chase....