The choice of the Dalai Lama's successor "belongs to the Tibetan Buddhists and not the Chinese government", Brownback told AFP.
But Beijing responded angrily, saying the US is attempting to "meddle in China's internal affairs under the pretext of religious freedoms".
"It is doomed to fail and will certainly be met with opposition from the international community," Chinese foreign ministry spokesman Geng Shuang said at a regular press briefing in Beijing.
China - which argues it has brought modernisation and development to the Himalayan region - has increasingly hinted it could name the next Dalai Lama, who would presumably be groomed to support Chinese rule.
The Chinese government has also indicated it is waiting out the Dalai Lama, believing his campaign for greater Tibetan autonomy will end with him.
At age 84, the spiritual leader who once travelled incessantly has slowed down and earlier this year suffered a chest infection, although he is not known to have serious health issues.
In 1995, the officially atheist government selected its own Panchen Lama and detained a six-year-old identified for the influential Buddhist position - whom rights groups called the world's youngest political prisoner.
Mindful of Beijing's plans, the 14th Dalai Lama has mused about breaking with the centuries-old tradition in which wandering monks look for signs that a young boy is the reincarnation.
The Nobel Peace Prize winner has said that he could pick his own successor, possibly a girl, or even declare himself the final Dalai Lama.