The West London side's first win of the season over Fulham last weekend saw the club move up from the bottom of the league table, but the Rs are still five points adrift of safety even after Redknapp replaced Mark Hughes on the bench.
Redknapp believes that the 33-year-old Anelka, said to be departing Chinese club Shanghai Shenhua, could help fire his side to safety, providing the terms suit both the club and the player.
"[Anelka] is a player that is of interest to anybody. I think he is finishing in China so he is available," Redknapp told reporters. "He is a top player, so he is a player we would be interested in, but whether we could afford to get anywhere near him, I am not sure."
The French striker has plenty of experience in the Premier League, having represented Arsenal, Liverpool, Manchester City, Bolton and Chelsea, but he has struggled with just three goals in 22 appearances for Chinese side Shanghai Shenhua.
Even though Redknapp believes chairman Tony Fernandes has contacts with the striker's agents, he stated the deal hinges on whether the outlay would be beneficial to the club.
"I think the chairman knows Nicolas' people and that so has got a few details on what it would be," Redknapp said. "It depends, as I say, just how expensive the whole package comes to. If it is within reason, he is a player that could certainly improve your team. There is no doubt about it.
"It is what you can do, whether you can afford these players, what they are looking for, whether they are reasonable, whether you can deal with them and most importantly whether you think they can do the job you want."
The Rs are unbeaten under Redknapp with three draws and a win, and have 10 points after 17 games with upcoming fixtures against Newcastle, West Brom, Liverpool and Chelsea seen as crucial to their survival.