Sunderland had recently placed a bid of around £5million for Downing but it was rebuffed by the Hammers.
The Black Cats are set to return with an improved offer but they will now face competition as Leicester have expressed their interest in signing Downing.
Sunderland are still said to be in the driver's seat to land Downing as he is looking to make a return back to his native North East but the Black Cats will have to match the Foxes' offer in order to convince West Ham into parting with the ex-Liverpool and Aston Villa man.
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