Rowett is convinced he has one of the best keepers in the division in Randolph and wants him to remain at St Andrews behond the end of the season when his contract is due to expire.
"I have spoken to Darren, I have spoken to his agent and certainly we are wanting to keep him for longer," the Blues boss has told the Birmingham Mail.
"Like any player that's out of contract at the end of the season and you are so close to January, I think most players just want to see if there is something higher.
"Every player in my team is ambitious and I want them to be ambitious and if a Premier League club comes in for Darren Randolph, then fantastic.
"But we would love to keep him and I think he's one of the best goalkeepers in this division."