The London club are bottom of the Premier League table with only four points from their first eight games after a dramatic 3-2 defeat against Liverpool on Sunday.
Redknapp has had to fend off questions about his future, as Tim Sherwood has been linked with the Loftus Road hotseat.
The experienced Redknapp is unperturbed by speculation that he could be sacked by chairman Tony Fernandes.
"I couldn't give a monkey's," said the former Tottenham manager.
"If it ain't good enough, it's up to other people to make their mind up.
"I don't go home and worry about speculation, I'm 68 nearly.
"What am I worried about? I'm not 35 with five kids trying to pay a mortgage.
"I love my job, and I do my best: I can't do any more and there's no one could do any better here at the moment than me.
"I hear other names mentioned, but they couldn't do any better than what I can do, that's for sure."
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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
