The Northern Ireland international has impressed hugely over the past 12 months.
Per the Belfast Telegraph, Bournemouth, Leicester City, and Villa are among the teams chasing after Hume.
The right-back played 46 times for the Black Cats in the past campaign, becoming a key player.
Speaking to the Belfast Telegraph, Hume said: “I think I could play in the Premier League. You have to keep yourself at a high standard and you want to push yourself as much as you can.
“That’s the level I want to get to but I’m happy enough at Sunderland and happy where I’m at and I’m really enjoying my football. If a move happens, it happens and if doesn’t I’m happy to play for Sunderland.”
When asked about transfer speculation, Hume said: “I try not to think about it. I let my agent deal with all that stuff and until they come to Sunderland and offer money I don’t pay too much attention to it.”