Austin's seventh Premier League goal of the campaign helped see off Leicester City on Saturday, with the 25-year-old continuing to impress in his maiden top-flight campaign.
The former Burnley man's form has seen him tipped for an England call-up in recent weeks as well as a transfer elsewhere.
However, despite Austin's current deal expiring at the end of next season, Redknapp does not see his contract as a pressing issue.
Asked on whether the club would be eager for Austin to pen fresh terms, he replied: "I'm sure the club would but I don't get involved in that.
"That's on the chairman's side, I'm sure everyone wants to keep Charlie here and I'm sure they'll be sitting down talking to him.
"I've never discussed it with him. I don't know how long he's got left on his contract. He's going well but he needs to keep going well.
"He needs to get 20 goals this season and I think he's capable of that. He's a great lad as well."
Austin's winner at the weekend took QPR off the bottom of the table with Redknapp's side now tasked with gaining a first away league win of the season against Swansea City on Tuesday.
"We're in good form but we need to pick up points away from home, that's the key for us," he added.
"Every game is difficult, it'll be a tough game. We've had some tough away games, certainly away none have been easy. All the teams [we have faced] have been bang in form but we've got to go pick up points away.
"You have to go work very hard to stay with [Swansea], they play some great football but it's about time we got an away win so we have to be positive that we can go and get it."
