The company has said it would create a standalone unit for its shopping service and make it compulsory for the unit to bid against its rivals for ads which are displayed at the top of its search page, Bloomberg reported quoting people said to be in the know.
The report said while the unit would be part of Google, it would function separately and bid for ads using its own money.
The EU fined the company €2.42 billion (US$2.7 billion) in June over the shopping service and ordered it to end its behaviour within 90 days or else face penalties of up to 5% of the daily worldwide turnover of Alphabet, its parent company.
A third investigation, into Google's Adsense advertising service, may also bring a fine; the EU is said to have made a preliminary determination that Google has abused its dominant position.
Bloomberg said that Google would make changes to an advertising panel at the top of its search screen that displays product images with links to the websites of retailers. Ten slots would be present and these would be auctioned to give rival sites a chance to buy space.
Google Shopping will also be able to bid for these slots but it will have to do so using its own revenues.
The EU's findings have been challenged in court by Google.
But Google's rivals did not appear to be happy about the proposed remedy. Kelkoo chief executive Richard Stables told Bloomberg that the proposal was worse than what had been suggested to settle the matter in 2013.
He added that if anyone thought such a change would resolve the issues in the online shopping space, then they clearly did not understand how the market worked.
British shopping site Foundem last week said: "Unless Google is volunteering to break up its general- and specialised-search businesses, the inclusion of Google’s comparison shopping competitors into a new or existing pay-for-placement auction would simply create an additional anti-competitive barrier — one that would formalise the transformation of free, relevance-based traffic into paid, pay-for-placement traffic for all services but Google’s own."