The Daily Star Sunday says Richards is frustrated at not commanding a regular role, with Pablo Zabaleta ahead of him in the City pecking order.
Richards, 25, will monitor the situation between now and the end of the season.
But that will not stop Arsenal from preparing a move for the £10million-rated defender, who has also lost his place in the England set-up, not featuring for his country in the last three years.
Arsene Wenger has been a long-time admirer of versatile Richards, who can play either at right-back or in central defence.
But the Gunners boss will have tough competition if Richards is up for grabs in the summer.
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