City have already secured Nathan Ake from Bournemouth and want to sign another centre-half.
Otamendi and John Stones are two who could make way.
The Sun reports that City want Otamendi out so badly they are halving the asking price for the player to roughly £8 million.
The Argentina international has played 210 games for City, but has not impressed this season and is seen as surplus to requirements by manager Pep Guardiola.
His wages coming off the wage bill would also free up room to sign additional players as the club looks to win the Premier League next season.
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