The Mirror says Richards and his representatives have been negotiating for more than a month over an improved deal to reflect the defender's new-found worth following his rapid progress with City and England.
While the Eastlands club are happy to make the new deal less reliant on bonuses, they have refused to entertain the prospect of allowing Richards a getout clause in the contract.
This is because Oldham are entitled to 20 per cent of any fee under the terms of the deal they struck with City two years ago.
If City agreed to a clause stating Richards is free to talk to clubs who offer a specific amount, that would reduce their ability to get the best price for their prized asset.
The defender is currently valued at around £20million, but City would want around £25m for him to compensate for the amount they are obliged to pass on to Oldham.