These trading firms had floated separate tenders on July 13 on behalf of the government.
PEC has received 15 bids in a price range of USD 270-297 per tonne for its tender of 90,000 tonnes and Singapore-based Starcom was the highest bidder, sources said.
STC, which had floated a tender for export of one lakh tonnes of wheat, got 12 bids in the range of USD 260-302 per tonne with Germany's Toepfer International being the highest bidder, they added.
MMTC received five valid bids in the price range of USD 265-280 per tonne for 90,000 tonnes of wheat export.
According to tender documents, STC is offering wheat from FCI stocks at Mundra port, while MMTC from Pipavav port and PEC from Kandla port.
The Cabinet Committee on Economic Affairs (CCEA) had last month allowed two million tonnes of wheat export from its godowns to ease storage problem.
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Wheat exports through private trade were already allowed in September 2011 and about 1.8 million tonnes of the grain has been shipped since then.
India produced a record 93.90 million tonnes of wheat in 2011-12 crop year (July-June). The government is facing a storage crisis because of record 82 million tonnes of foodgrains in its stocks against storing capacity of 64 million tonnes.