The Black Cats boss allegedly wants the Italian at the Stadium of Light.
David Moyes has just signed Chelsea centre-back Papy Djilobodji from Chelsea but he is thought to already be targeting more defensive recruits, with Gazza Mercato claiming that he wants to sign Torino full-back Davide Zappacosta.
Djilobodji is the only player to arrive through the entrance doors at the Black Cats so far this summer, but Moyes wants more additions as he looks to strengthen the squad which narrowly avoided relegation last term.
Numerous targets have been speculated, but the latest name to emerge on the grapevine is that of Italian full-back Zappacosta.
The 24-year-old only joined the Turin side last summer but impressed in his first season for the club, scoring once in 25 Serie A appearances.
Though he is yet to win a senior cap for his country, that form saw him rewarded with a first call-up to the squad as he was named in new Chelsea manager Antonio Conte's provisional 30-man group for Euro 2016, ultimately being left on the stand-by list.
Gazza Mercato claim that Zappacosta is high on Moyes' list of full-back targets, but any deal could be a tricky one to complete.
That is because Torino are not looking to cash in on the star, and are likely to do all that they can to hold on to the man who has been tipped by some in his home country as a future full-back for the Italy senior side.
However, Moyes will be keen to add further reinforcements ahead of the Premier League opener at Manchester City at the weekend.