The newspaper, quoting anonymous sources familiar with the matter, said the expected transaction could be worth up to $1.75 billion.
The stake will be from the Munjal family, which controls Hero Honda.
Last year, Japan's Honda Motor sold its 26 percent stake in the Indian firm to the Munjal family at a steep discount, the Financial Times said.
India, the world's second most populous nation, is a major market for motorcycles, and last year Hero Honda produced nearly five million of them, the report said.
GIC is one of Singapore's two sovereign wealth funds -- along with Temasek Holdings -- and invests the country's massive foreign reserves of well over $100 billion.
It does not publicly give a value on its holdings but the US-based Sovereign Wealth Fund Institute ranks it as the seventh largest in the world with an asset portfolio valued at $247.5 billion.