The Ukraine international is on-loan at Forest from Arsenal, but isn't in the plans of manager Sean Dyche.
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Dyche confirmed last week that talks were underway with Arsenal to cut short the season-long deal.
De Telegraaf says Arsenal have already found a new club for Zinchenko in Ajax.
Zinchenko himself is not averse to the deal, but still needs to approve it.
It could transform into a long-term move, as the Ukraine midfielder's contract expires in the summer.