Chinese Foreign Minister Wang Yi made the proposal during talks with his counterpart in Dhaka in a move which local exporters described as a "huge development".
"The Chinese minister has offered to sign a free trade agreement," Bangladesh Foreign Minister Abul Hassan Mahmood Ali told reporters.
"The Chinese government is well aware of the existing trade gap and they have assured us they want to minimise it," Ali added after meeting Yi.
The Bangladeshi minister did not say whether Bangladesh would sign up to any such agreement.
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Two-way trade between Dhaka and Beijing soared to USD 8.3 billion in the financial year ending in June, but exports from Bangladesh accounted for less than a tenth of the total.
Bangladesh is a signatory to several multilateral free trade agreements but has yet to sign any bilateral FTA.
The country's garment industry welcomed the Chinese offer, saying it could "massively boost" exports to the world's second largest economy. Bangladesh is the world's second largest garment exporter after China.
"Its domestic garment market is worth over $300 billion so one can imagine the kind of market access we have if Dhaka signs an FTA with Beijing," he said.
He added that thanks to some preferential trade access given by Beijing in recent years, Bangladesh's garment exports to China grew to USD 240 million in the last financial year, from less than USD 10 million in 2009-10.
Bangladesh's government is an ally of its neighbour India, but experts say Beijing has been attempting to woo Dhaka in recent years by increasing development aid.