Redknapp was keen to bolster his forward options at Loftus Road, but Toronto FC wanted to keep Defoe for their MLS playoff run and terms were not agreed with Borini.
The Liverpool striker was linked with a move to Sunderland but, as the deadline approached, QPR emerged as favourites and entered talks with the Italian.
But personal terms proved a stumbling block and Redknapp told Sky Sports that he was disappointed he was unable to make a third or fourth signing of the day after bringing in Sandro from Spurs and Niko Kranjcar on loan from Dynamo Kiev.
"Jermain wanted to come," Redknapp said. "We were hoping to get him. We agreed a deal with Toronto but it was difficult for them to release him.
"They are looking to get in the playoffs and we didn't want to disrupt their club or anything else so we moved on.
"Borini, we just couldn't do a deal with the player. We agreed a deal with Liverpool but we couldn't meet what the lad was looking for."
It's an odd situation. He clearly wants to play football but why does that have to be at Liverpool? Does he think he'll get ahead of Sturridge or Balotelli to play in Champions League games? Rodgers is often flexible with formations and sometimes plays with two strikers but you'd have to think that were two of the three currently ahead of Borini out of contention then Rodgers would go to one striker and three attacking midfielders before playing him in a front two. I might be harsh on him and he can move ahead of Lambert as you never know in football. But the likelihood is he'll only play when all the other strikers are out. From his point of view, what's the point in that?- thebigshow