The Mirror says Liverpool have now slashed their asking price for the Uruguary striker as they seek a buyer this summer.
The Reds will sell for €50m, with Napoli having already offered €43m in recent days.
The Azzurri are expected to return with an improved offer as they seek cover for prime centre-forward Romelu Lukaku.
A move to Saudi Arabia also cannot be discounted after Nunez was blocked by Liverpool in January from making a €70m move to Al-Nassr.