The Chelsea winger was shopped around by the Stamford Bridge club in the last weeks of the transfer window.
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While they were sent a proposal, West Ham are said to have turned down the opportunity to sign the forward.
The Independent states that Sterling was not felt to be a good fit within the club’s wage structure.
Arsenal are said to be paying at least half of his Blues wages, which are higher than £300,000 per week.
Sterling was also linked to Manchester United, who eventually loaned Jadon Sancho to Chelsea with an obligation to buy.
