Either the opening batsman Sanath Jayasuriya or Roshan Mahanama will lead Sri Lanka in next month's triangular series with Australia and India, while Mahela Jayawardena is tipped as a possible deputy.
The appointments are expected to be officially announced on Monday.
"The need for a change at the top became apparent following Sri Lanka's dismal run in the last five one-day tournaments...culminating with their unsuccessful attempt to defend the World Cup in England last month," reported Colombo's Daily News.
Ranatunga has been Sri Lanka's most successful captain, leading the country in 193 one-day matches in an 11-year career in which they became world champions in 1996. It is thought that Ranatunga will be asked to quit the captaincy so he can leave honourably.
The decision on Ranatunga follows remarks by the sports minister, S B Dissanayake, who was reported as saying he did not see him as a future captain.
Dissanayake, in an interview with the BBC, claimed Ranatunga "got many things wrong in the tournament. He made several bad decisions... in future I believe he will play in the team but not as a captain."
Sri Lanka's miserable World Cup ended with them having lost to England, South Africa and India, and beating only Kenya and Zimbabwe.Reuse content