The France international was among those moved out of Loftus Road following QPR's relegation out of the Premier League.
He is due to spend the 2013/14 campaign at St James' Park, with his future then due to be reassessed next summer.
Redknapp claims he would be happy to see Newcastle take up their option on Remy and would also be willing to talk terms with Fulham over another loanee, Adel Taarabt.
He said in the Shields Gazette: "Remy wanted to go to Newcastle, so good luck to him. I hope he does well.
"He's not in my thoughts. I only want people who are here and want to be here, that's all I'm concerned with.
"Taarabt and all those who've gone on loan, good luck to them.
"I hope they do well, stay where they are and get a contract there."