Australian fast bowler Brett Lee is back in training after ankle surgery and expects to start bowling again within six weeks.

Lee, 27, had the operation in March and said he hoped to be fit for the two-Test series against Sri Lanka in Darwin and Cairns in July.

"I will definitely make sure that I am ready for India though," Lee, who is in Singapore for an awards function, told Reuters on Thursday.

Australia are due start a tour of India in September, although the itinerary has yet to be confirmed.

Lee, who has taken 139 wickets in 37 Tests, came out in support of record-breaking Sri Lankan spinner Muttiah Muralitharan, who has been barred from bowling his controversial 'doosra' delivery by the International Cricket Council (ICC).

"He's a great talent and I can't see any reason why they can't let him keep bowling," Lee said

"As far as I see, he's a guy who really enjoys his cricket. I think that he means well."

Muralitharan, who became the highest wicket-taker in Test history earlier this month, has stopped bowling his 'doosra', which spins away from right-handed batsmen, after the ICC ruled he was illegally straightening his arm during the delivery.

"The reason why bowlers are getting more scrutinised these days is because of the technology. So we have to leave that up to the biomechanist to make up their mind in regards to his action," said Lee, whose bowling action has also been queried in the past.