The 25-year-old endured a season blighted by injury before Di Canio took charge in April, making just 14 appearances in all competitions.
Di Canio is in the midst of a complete squad overhaul on Wearside and does not view Cattermole as part of his future plans, according to The Mirror.
Cattermole joined the club for a fee of £6m in 2009 and was intent on fighting for his Sunderland future last month, putting off a holiday to focus on rehabilatation from knee surgery.
That commitment has not thought to have changed Di Canio's mind, with the Italian actively searching for new central midfield options in the close season.