Sri Lanka Cricket on Wednesday formally suggested to Australia to mark their upcoming Test series with a trophy named after spin rivals Shane Warne and Muttiah Muralitharan.
The country's governing body said they had written to Cricket Australia that the winner of the two-Test series, opening in Brisbane on November 8, be awarded the Warne-Murali Trophy.
"We have sent our proposals and have got a very good response," SLC secretary Kangadaran Mathivanan told AFP.
The SLC said it was confident that Cricket Australia would endorse the proposal to name the Trophy after two of the world's greatest spin bowlers.
Muralitharan is just nine wickets away from surpassing the retired Warne's world record of 708 Test wickets.
Sri Lanka last played a Test series in Australia in 2004 and the next contest may not take place before 2010.
Cricket Australia spokesperson Peter Young said the trophy should be finalised by the conclusion of next month's two-match series which will mark the 25th anniversary of Tests between the countries.
"There have been discussions between Australia and Sri Lanka for two or three years about introducing a perpetual trophy of the Border-Gavaskar type," Young said in Melbourne on Wednesday.
"We are particularly conscious that the coming summer marks the 25th anniversary of Australia-Sri Lanka Test cricket.
"And we are very keen to formalise and finalise an appropriate manner for celebrating that and building further on the tradition that has grown between Australia and Sri Lanka.
"We would expect to be in a position to formalise and finalise that by the end of the series."