TMW says Bologna have accepted a €50m offer for the Italy international.
The Gunners have burned off competition from across Europe to land Calafiori, with Bologna agreeing terms knowing 40 per cent of the fee will be due FC Basel.
Arsenal upped their offer on Wednesday afternoon after Bologna chief Joey Saputo having rejected a €47m bid earlier this week.
Bologna chief Giovanni Sartori hinted on Monday morning: "We are talking to Juventus but also about many other teams. At this moment we will try to keep him. If requests arrive we will have to think about it, I'm not saying that we will give him because the president has exposed himself by saying that he wants to keep the whole team, but we will certainly make some evaluations.
"I don't think he will go to Juventus, he will probably go to a different market, but I repeat that we would like to try to keep him. Calafiori had a great European Championship, it's a shame it didn't help Italy. Now let's let him rest, then we'll see what happens on the market."