"There is no such thing. No one has asked us to host the Asia Cup," Ranatunga said. "The original decision of the ACC (Asian Cricket Council) stands.
The Asia Cup is due to begin in Bangladesh on February 25 and the finals will be on March 8.
The Twenty20 World Cup, which features all of the major teams in international cricket, is to run from March 16 to April 6.
The three venues chosen for the T20 tournament -- Dhaka, Chittagong and Sylhet -- have all experienced violence over the past month.
In 2009, during a trip to Pakistan, the Sri Lankan cricket team was ambushed by armed gunmen in an attack that wounded a number of players and killed at least six policemen.
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"We are very positive about playing in Bangladesh," Sri Lanka Cricket (SLC) secretary Nishantha Ranatunga told AFP. "We look forward to playing there.
Confirmation that the tour is going ahead comes after SLC vice president Mohan de Silva and the board's former chief executive Ajith Jayasekera travelled to Bangladesh ear