The Daily Mail says the powerful midfielder is already an ambassador for the sportswear giants, having agreed a boot and kit deal with the firm in 2011.
But PUMA chiefs are keen to tie the Ivory Coast international to a new contract, with preliminary talks understood to have already taken place.
Toure has been a key figure in boosting PUMA's appeal in Africa, a key selling point for the firm.
And the fact PUMA are also kit suppliers to the Ivory Coast national team makes Toure central to their promotional plans.
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