Shakhtar could offer Allegri a four-year contract worth €6m a season - a big increase on his current €2.5m-a-season deal at the San Siro, which is due to expire next summer.
Allegri has also been linked with a move to Roma, but Shakhtar have the finances to tempt him to the Donbass Arena.
Shakhtar have been managed by the former Inter and Romania coach Mircea Lucescu since 2004.

