The Tottenham midfielder is facing stiff competition for a starting berth at White Hart Lane this term following the close-season signing of Paulinho.
However, Redknapp, who signed Parker when he was in charge at Tottenham, is keen to have the England international with him at Loftus Road as QPR aim to win promotion back to the Premier League at the first attempt.
"We're hopeful of getting Scotty signed soon," Redknapp said.
"He's a great lad and will be a really good signing for us."
Parker made only 23 appearances in all competitions last season after the beginning of his campaign was disrupted by injury.
The 32-year-old was named the Football Writers' Association Footballer of the Year and England Player of the Year in 2011, shortly before Redknapp signed him for Tottenham.
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