Tharanga managed just 17 runs in his last three outings and his longest innings lasted no more than 22 balls -- a huge cause for concern.
Atapattu is a member of Sri Lanka's 15-member squad, but has not played in this World Cup.
"That's something we'll have to think about. He's hitting the ball pretty well but he's just not spending time out there in the middle," Sri Lankan captain Mahela Jayawardene told journalists in Grenada.
Sidath Wettimuny, a highly acclaimed opening batsman in the 1980s, said showing Tharanga the door to make way for Atapattu was "a very tough call to make.
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"It is the people on tour who are aware if Marvan has maintained the required levels of fitness and if he is batting well in the nets," Wettimuny told AFP in Colombo.
The former captain has not figured in any of the games so far and seems set to repeat the 1996 record of not playing a single game despite being a member of the champion squad.
Wettimuny, also a former chief selector, added: "