Having sacked Hughes earlier in the day, QPR opened discussions with Redknapp about him taking over a side which is in last place in the Premier League and without a win this season, having earned only four points from 12 games.
Late Friday night, Redknapp told British television channel Sky Sports News that he was keen to become QPR's new manager and that "hopefully we can get it done tonight. There shouldn't be any problems.
"If everything gets sorted, and I'm sure it will, I'll be in Sunday morning, will have the team in training on Monday, then fly up to Sunderland." QPR faces Sunderland on Tuesday in what would be his first match in charge.
Redknapp said he planned to go to watch QPR's match at Manchester United on Saturday. He also said he hoped to bring his two longstanding coaching assistants — Kevin Bond and Joe Jordan — with him to the west London club.
"I'm looking forward to it. It's a big challenge and a tough job to take on — but I'm up for the challenge," said the 65-year-old Redknapp.
Though widely acknowledged as a shrewd mover in the transfer market, he ruled out any major splashes when the transfer window opens in January, despite the very real threat of relegation.
"I don't think too much will happen in January," he said. "There is a big staff there and you can't keep bringing players in. The players have got to start performing. If they do that we've got a chance."
He said the team had to "find a way to pick up points, be hard to beat and win some matches. It's all about the players."
Redknapp took charge of Tottenham in 2008 when the team was last in the Premier League with only two points from eight games. He turned their fortunes around, guiding them into the Champions League for the first time in 2010.
He was fired in June despite Tottenham finishing in fourth place last season, and has since taken on a non-paid advisory role at third-tier Bournemouth and become a television pundit with the BBC.
Hughes was dismissed after failing to turn around a dismal run of results.
"Mark has shown integrity and professionalism throughout his time here, but ultimately the circumstances we find ourselves in have left the board of directors with very little choice but to make a change," QPR said in a statement.
Fans turned on Hughes — and the QPR players — after the loss to Southampton, which left the team five points from safety with nearly a third of the season gone.
"Maybe it's a watershed moment because we can't get any lower," said a despondent Hughes, who had 1 1/2 years left on his contract.
Tellingly, QPR owner Tony Fernandes refused to defend Hughes last weekend, as he has done in recent weeks. Only last Friday, Fernandes posted a Twitter message responding to calls for Hughes' departure, saying: "Won't be happening. For the one millionth time. Hahaha. Stability."
That changed this Friday.
"This decision has been taken after careful consideration by the board of directors, following numerous meetings over the last few days," QPR said.
Assistant coaches Mark Bowen and Eddie Niedzwiecki will take charge of QPR's match at United.
Hughes managed to keep QPR in England's lucrative top league thanks to a strong finish last season and attempted to revitalize the squad by signing 11 players in the off-season, including Park Ji-sung from Manchester United, Jose Bosingwa from Chelsea and Julio Cesar from Inter Milan.
Getting so many new players to gel has been his major problem, while the team has struggled to score and also has one of its leakiest defences.