Redknapp is keen to bolster his midfield in this month's transfer window and he is a big fan of Palacios having signed him during his time in charge of Tottenham.
Palacios has fallen out of favour at Stoke and has made just four appearances for Tony Pulis' side this season.
Stoke are willing to offload the Honduras international and Palacios' father, Eulogio, claims Redknapp is keen to be reunited with the 28-year-old at Loftus Road.
"Wilson is going to join QPR. Their manager is interested in signing him once more, as he knows him well," Palacios' father is quoted as saying in The Sun.
"Wilson is going to change clubs as he is not getting games for Stoke. Their manager puts him on the teamsheet but does not play him."