Calciomercato.com reports the two Italian giants are keen on the player who is out of contract this summer.
Hendrick is likely to depart the Turf Moor club on a free transfer.
The Republic of Ireland international may still renew with Burnley, but if he does move then Italy is the most likely destination.
The player only wants £1.8million-per-year, which appeals to both cash strapped Italian clubs.
It is unclear if there is any interest from Premier League teams in Hendrick.