The Rangers manager attempted to send Mauro Zarate back to West Ham United and asked the Hammers if he could have Matt Jarvis instead.
However, the Premier League confirmed rules were in place to prohibit Zarate from returning to his parent club within the same transfer window.
It emerged Jarvis was also unable to make the move across London as top-flight clubs cannot secure more than one player from a divisional rival.
Redknapp had earlier made enquiries for Tottenham’s Aaron Lennon and Emmanuel Adebayor but ended up landing none of his targets.
The QPR boss is now left with Zarate, who was effectively deemed surplus to requirements by the deadline day wrangle, as his only winter arrival at Loftus Road.
Zarate’s fitness is a concern to the Hoops and the Argentine striker has so far failed to feature for 90 minutes since joining on a loan deal.
Summer signing Jordon Mutch’s sale to Crystal Palace was Redknapp’s most notable piece of business as QPR continue their battle for Premier League survival.
Next up for the Hoops is the visit of fourth-placed Southampton on Saturday.