Richards, 19, is due to meet City for contract talks once the transfer window closes on Thursday, when he will be told the club are not prepared to break their pay structure to give him £70,000 a week.
He will then have to decide whether to accept a long-term deal for about £50,000 a week or leave in the summer. Indications are that City's ultimatum may work and the player will drop his initial demands and sign.
The deal offered by City would make him the highest-paid player at the club, but it is below what many of his team-mates in the England dressing-room would earn.
Richards has two-and-a-half years left on his current deal and delayed talks because he was in the process of changing agents. His availability would create the hottest transfer chase of the summer, with Avram Grant, Arsene Wenger and Sir Alex Ferguson all huge fans.