Hughes paid with his job on Friday for Rangers' failure to win any of their opening 12 Premier League games.
And talks are ongoing with Redknapp, who has been out of work since leaving Tottenham at the end of last season.
The 65-year-old is the only candidate being considered for the job and can no longer be backed with Sky Bet to take charge at Loftus Road.
In the meantime Hughes' assistants Mark Bowen and Eddie Niedzwiecki will be in charge for Saturday's trip to Manchester United.
A spokesman for Redknapp's agents, Paul Stretford's Triple S Sports and Entertainment, said: "Contact has been made between QPR and us as Harry Redknapp's representatives."
QPR owner Tony Fernandes backed Hughes consistently until last week's home defeat to Southampton, and the supporters' angry response to that result apparently influenced his decision to change manager.
Fernandes tweeted: "This is a club where the chairman and shareholders look at all things in a long term view but also take the views of the fans who are the most important constituents of the club. To us fans come first."
Redknapp has been out of work since leaving Tottenham in June and he has been linked with a number of jobs since, but he is now poised to get back into management at Loftus Road.
Hughes only narrowly avoided relegation after taking over from Neil Warnock in January.
A QPR statement read: "The board of directors wish to thank Mark for his commitment, hard work and dedication in his ten months in charge.
"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.
"The board will now be working actively to put a new managerial structure in place as soon as possible."
Hughes' final game in charge was a demoralising 3-1 home defeat to newly-promoted Saints, who cut their hosts four points adrift at the bottom of the Premier League.