The Championship side have had a bid accepted for the 25-year-old striker, who scored 29 goals in all competitions for the Scottish champions last term.
Redknapp, who is looking to oversee the club's return to the Premier League after suffering relegation in 2012-13, believes that he is not too far away from getting his man - although reports suggest that Norwich may now have also entered the race for the player's signature.
Whether rumoured interest from the Premier League club changes the situation remains to be seen, but Redknapp told BBC Radio Scotland: "It looks like it's on its way to being done. Negotiations have gone well."
The former Tottenham boss also backed Hooper to be a success at Loftus Road, should a deal be finalised.
"He's a finisher. He'll score goals in the Championship, I'm absolutely certain of that," he added.
"He's gone to Celtic, one of the biggest clubs in the world, and he's scored goals. He's scored goals in the Champions League.
"If he can come here and get 25 goals next season, then we will have a real chance of getting out of the division."