The 43-year-old has been heavily linked with the vacant managerial position at Stoke, who sacked Mark Hughes after their humiliating FA Cup defeat at Coventry on Saturday.
But Rowett, who has led Derby to second in the Championship this season, committed his future to the Rams by agreeing a new three-and-a-half-year deal.
“Originally this was the job I wanted out of all the jobs out there,” he told Derby’s official website. “I’m massively committed to trying to finally get this team back into the Premier League.
“If you do what’s perceived as a good job, there’s always going to be speculation about other positions.
“There’s always going to be press speculation and stuff about other jobs, but my focus has always been on achieving something with this club. And that’s going to remain the focus.”
The Potters will now have to look elsewhere, with both Martin and Michael O’Neill liked, while Ryan Giggs is also in the frame.
Wigan boss Paul Cook thinks the Latics are being shown too much respect ahead of their FA Cup quarter-final against Southampton on Sunday.
The prospect of a first trip to Hampden proves it was a good decision to move to Scotland, says goalkeeper Jon McLaughlin.