Hysaj, 26, is out of contract in a year’s time and Napoli could choose to cash in on him.
Spartak have proposed a five-year deal worth €3m-per-season to the Albanian international.
Rino Gattuso values Hysaj, who has played the full 90 minutes in both of Napoli’s league games this term.
Hysaj contributed an assist in Napoli’s 6-0 drubbing of Genoa on Sunday.
A consistent performer since arriving from Empoli in 2015, full-back Hysaj has made 196 appearances for the Naples club.
Spartak are looking for reinforcements as they hope to challenge for the Russian league title.
After nine games, Domenico Tedesco’s side are in second place, behind leaders Zenit only on goal difference.