Club chairman Tony Fernandes said: "I had a positive meeting with Harry. I don’t think there was any point where he was thinking of not being with us."
"It was a good meeting because we are all very clear on the timelines, we’re very clear on what to do.
"We want players that want to play for us. Players that want to win. Players who get disappointed like I do when we lose. I haven’t said it because it wasn’t right, but it hurt me when I saw some of the players who didn’t feel the way I felt."
He added: "It wasn’t right to say anything during the season, but I noticed everything and I am a little bit wiser for it now."
Redknapp said: "We're going to give it a real good go next season and hopefully get this club back to where it belongs. We've got to re-build and get a team together that can be really competitive in the Championship."
Rangers dropped into the Championship after a goalless draw with Reading at the weekend, with Redknapp quick to highlight a lack of time with his players as a factor in their failure to retain top-flight status.
The former West Ham and Tottenham boss had been installed as the bookies’ favourite to be the next Premier League manager to leave his post, but the club have now moved to quash any speculation.
Redknapp had already moved to ease the pressure on his side ahead of next season's campaign, insisting that the quality of the Championship will make life very difficult.
"Next year will be a big challenge as there are a lot of good teams and massive clubs in the Championship," he said.
"There are big clubs who have all been in the Premier League before and we are just one of them.
"There is a lot of hard work to be done this summer. It's a really good challenge, it's possible, but it's not going to be easy."