The 19-year-old midfielder, a target for Bournemouth during the last transfer window, has just one year left on his current contract.
But Rowett told the club website: “We have had very good discussions with his representatives. We are hopeful that the player wants to stay.
“There has been an indication that Demarai likes the club, he likes living locally, he likes what the club have done for him – and he would like to stay.
“I think that would be good for his career. As with all of these deals it’s down to whether we can find a solution that fits all parties.
“He is a player there has been an immense amount of speculation about; we have had good bids for him.
“It’s always a situation with a player like him that we have got to fight hard to keep him because we want to send a good message out to the fans and we also want the team to be as competitive as possible next year and we see Demarai as being a huge part of that.”