The rupee headed to a one-week low against the dollar on Wednesday following a report from a major regional newspaper that Reserve Bank of India Governor Raghuram Rajan did not want to remain at the central bank, citing unidentified sources.

The rupee fell to as low as 67.45 per dollar, down 0.3 per cent from its close, after Anandabazar Patrika, a Kolkata newspaper, reported that Rajan would prefer to go back to the United States after his three-year term expires in early September, citing sources close to him.

The RBI did not immediately reply to requests for comment. Foreign investors have been on edge about whether Rajan, a former chief economist at the International Monetary Fund, will be re-appointed by the government for a second two-year term.

Reuters on Wednesday reported the government would re-appoint the governor, should he wish to stay on, citing government officials. Rajan has previously declined to say whether he would accept such a re-appointment saying it would be speculative to discuss.

Still, most analysts expect Rajan will remain at the helm of the RBI for another two years, and despite widespread speculation, markets have not been significantly hit by fears he would leave in September.

"Some rumours that the governor may not go for a second term led to reducing of short positions," said Ashtosh Raina, head of foreign exchange trading at HDFC Bank in Mumbai.

"Otherwise the rupee was expected to be strong today on the good GDP numbers."

India on Wednesday said gross domestic product expanded at a stronger-than-expected rate of 7.9 percent, extending its lead as the world's fastest growing large economy.

Rajan has been popular with foreign investors who cheered him for his efforts to lower India's inflation and clean up state-run banks' massive bad loans.

But he has also attracted the opposition of some local politicians for not lowering interest rates enough, raising some concerns about his future.