The striker has impressed while on loan at St James' Park, scoring 10 goals in 19 appearances, and is expected to attract interest from elsewhere in the summer
The France international has impressed while on loan from the Championship outfit, scoring 10 goals in 19 appearances in all competitions for Alan Pardew's side.
The 27-year-old - who cost QPR around £8 million (€9.6m) in January last year - is up for sale and Redknapp feels Newcastle will have competition for the striker's signature in the summer.
"I don't know what the deal is. You'd think they'd want to snap him up, wouldn't you?" the Englishman told West London Sport.
"If they don't then someone else will. For what we got him for, he's probably worth double that now.
"He's scored goals in the Premier League again this year."
QPR could wait until the end of the season to sell Remy - and keep him if they are promoted to the Premier League - but Redknapp would be happy to get rid of the forward this month.
"That's all ifs and buts," he added. "You've got to get there first, and if someone came and offered £15m (€18m) or £16m (€19m) for him I'd sell him if it was my choice, but it's not - it's down to the chairman."