And the Hoops manager feels Parker would be a massive coup for the Championship side, having worked with the out-of-favour England international during his reign at White Hart Lane.
“We’ve made a good offer to Scott. We’ve agreed terms with Tottenham,” Redknapp said.
“It’s up to Scott now and what he does. We would love to have him here. We’ve made the offer and it’s up to Scott if he wants to come here or not.
“There’s an agreement with us and Tottenham but not with the player. If someone else comes in, he can go where he wants. We made him an offer – a good offer – but it’s up to Scott what he does.
“The chairman agreed a deal with Daniel Levy and now it’s up to Scott to make his mind up if he wants to come here or go somewhere else.”
Parker, 32, may have reservations about dropping down to the Championship a season before the World Cup in Brazil.
But the QPR boss feels a drop down to England’s second tier could provide Parker with a new lease of life.
“We feel we’re a club that are looking to get back up [to the Premier League] if we can this year,” he added.
“If you talk to Paul Merson, probably the best year of his career was when he joined me at Portsmouth and we won the league [Championship] and got promoted.
“I think sometimes you can have more enjoyment playing for a team that wants to go somewhere than a team that is hanging on in there with no real chance of winning anything or being in a battle to stay in the division.
“We feel like we’re a club that wants to progress and we’d love him to be part of it.”