Reports had hinted that the veteran boss would leave Loftus Road after their relegation from the Premier League was confirmed yesterday afternoon.
"Of course I'm serious. No-one is more serious about their football than I am. I signed a contract here and it has not entered my mind [to leave]," Redknapp told Sky Sports News.
The news of Redknapp's stay broke after he had held a meeting with Fernandes. Speaking about those discussions, Redknapp revealed that plans are already underway about the shaping of the playing squad.
"It was all positive. We've got to get prepared for a year in the Championship - a tough year. It's a very tough division - there's some big, big clubs in there who want to be in the Premier League," he added.
"You couldn't work for people who back you more than the people at this club. We've got a lot of players here and we've got to decide who we want to keep and who we want to move on. There's some good players here that we really want to keep.
"It's been hard work but we weren't good enough. We were short in certain areas. We're going to finish in the bottom two - that's where we deserve to be and that is how good the team was."
Redknapp was appointed to the QPR helm in November last year.