But at the same time, he said, whether or not there is a next reincarnation will depend on the Tibetan people's wishes.
"If it would be more useful, the Dalai Lama could certainly be female, but whether or not there is a fifteenth reincarnation will depend on the Tibetan people's wishes," he told reporters in Australia Thursday, said a post on his official website.
He was responding to a query on whether the next Dalai Lama might be a woman.
On the spate of self-immolations in Tibet, he said "the situation as very, very sad".
"These drastic actions are the symptom of a cause, which the Chinese authorities should investigate and take steps to resolve," he said.
On the one hand there have been 60 years of development and yet there remains deep dissatisfaction, and on the other the people who have taken these steps could just as well have harmed others, but chose instead only to harm themselves, the 77-year-old Nobel laureate said.
"They're very important. They allow people to get a clearer view of reality. This is why we have to be objective and truthful, rather than manipulative, with the information we share," the Dalai Lama replied on use of social media.
The globetrotting monk, who believes in the "middle-path" policy that demands "greater autonomy" for the Tibetans, reached Sydney Thursday for an 11-day visit for his teachings and a series of public lectures there, say his aides here.
The Dalai Lama now lives in exile in along with some 140,000 Tibetans, over 100,000 of them in different parts of India. Over six million Tibetans live in Tibet.
The Tibetan exile administration is based in this northern Indian hill town but is not recognised by any nation.