The former Arsenal man was recently released by Shakhtar Donetsk after four years in Ukraine, and is on the lookout for a fresh challenge.
The Super Hoops look set to lose Loic Remy on a permanent basis in the coming weeks, and Redknapp is looking to get fresh option to Loftus Road in a bid to avoid an immediate return to the Championship from the Premier League.
Eduardo is an appealing option with a lack of a fee needed, and his knowledge of the English game.
The Brazilian-born forward starred for Arsenal earlier in his career, netting 22 goals in 67 showings between 2007 – 2010.
However his spell in north London was plagued by injury, with the infamous Martin Taylor leg-breaking tackle a standout moment.
Interest from Turkey is high, while West Ham and Stoke are also thought to be considering the 31-year-old.