House of Fraser could face fines after the OFT alleged that the store group collaborated with Oakley between November 2001 and March 2004, agreeing to sell the sunglasses at prices no lower than those set by Oakley.
The investigation by the OFT was prompted a number of complaints from consumers and a retailer.
A statement released by the competition watchdog read: 'The OFT has provisionally found that Oakley and House of Fraser entered into an agreement and/or concerted practice to fix the minimum prices of Oakley sunglasses.'
If the accusations are upheld, they will fall under and be a breach of the Chapter I prohibition of the Competition Act 1998. House of Fraser could face a multimillion penalty of up to 10 per cent of turnover.
The sunglasses are popular with sportspeople, especially cricketers. Oakley UK director and general manager John Pollard said: 'We believe that the investigation by the OFT is based on a misunderstanding.'
The findings unveiled today are a preliminary decision and House of Fraser can respond before the OFT makes its final ruling by next summer.