The 22-year-old winger has been deemed surplus to requirements by the Tigers, with Steve Bruce allowing him to link up with Championship outfit Charlton Athletic on loan.
A short-term agreement is due to expire in January, at which point Stewart will be due back at the KC Stadium.
He sees little point in returning to the Premier League ranks, with his contract running down and no offer of fresh terms put to him.
Instead, Stewart would like to see his loan extended at The Valley or Hull take the decision to cash in on his services and allow him to find 'security' elsewhere.
He said in the Hull Daily Mail: "If there was the chance of extending my loan here I'd look at doing that. I think a lot of the gaffer (Chris Powell) and I hope he feels the same way. But if Hull need some money, maybe they'll want to sell me.
"If there is a permanent deal then it will give me a bit of security rather than a summer of thinking 'where am I going to go next?'. But it's not just what I want. It's about what Charlton want or Hull want - finding a balance.
"If it was just down to someone to choose to go on loan, then I'd prefer to stay here.
"This loan wasn't about Hull sending me out to see if they wanted me back. My contract is coming to an end at Hull and once it ends, that will be it.
"I've not heard anything from Hull. That might be a surprise to other people but it isn't to me. But it doesn't really affect me. I came to Charlton to play football - I don't need a well-done pat on the back from Hull.
"I had a great time at Hull and it's great to see them doing well in the Premier League, but if there was any chance of them extending my deal then I'm sure I'd have heard something by now."