The claims relate to the Shock Absorber bra, once advertised in a campaign featuring tennis player Anna Kournikova with the slogan "Only the ball should bounce".
The Office of Fair Trading (OFT) alleges that lingerie maker DB Apparel UK entered into anti-competitive agreements with John Lewis, Debenhams and House of Fraser between 2008 and 2011.
These were designed to increase the retail price of Shock Absorber bras in each of the three stores, applying on a national basis to a number of products within the range, it is claimed.
The regulator said it was one of the leading UK brands with 15% of the market at the time.
It said that its provisional view was that each of the alleged nine agreements amounted to resale price maintenance, in a "serious infringement of competition law".
Resale price maintenance occurs when retailers agree to a re-sale price set by product suppliers.
Ann Pope, OFT senior director of services, infrastructure and public markets, said: "The OFT takes allegations of price-fixing seriously.
She said the regulator would consider representations from the accused companies before making a ruling - expected by next March - on whether there had been a breach of competition law.
DB Apparel said: "We reject any allegations by the OFT that we have entered into any agreement or understanding with retailers as to their retail prices of our products.
"We have been transparent with UK authorities since the beginning of this process and will continue to defend ourselves vigorously in this investigation."
House of Fraser said: "We are co-operating fully with the Office of Fair Trading and the ongoing investigation and will respond accordingly.
"We are confident that we have been operating within all laws and regulations and are very supportive of any initiative which ensures pricing policies are fair for our customers."
Debenhams also denied the allegations.
It said: "Debenhams disputes these provisional findings of the OFT, but is not in a position to comment further at this stage. The matter is being dealt with by its external lawyers."
Current prices of Shock Absorber bras are advertised ranging from £25 and £38 online at Debenhams.
John Lewis said: "John Lewis always strives to operate within the law and comply with regulations.
"We are fully cooperating with the OFT and will respond in due course."