The newspaper claims that the 67-year-old wanted to sign the striker last summer but stands a stronger chance this time around as the Norwich City forward would like a return to the Premier League.
Hooper scored eight times in 23 starts for the Canaries last season.
In the same report, the Mirror affirm that the Rs are interested in Kolbeinn Sigthorsson - an already widely reported target.
The Evening Standard are reporting on similar lines, suggesting that Redknapp is holding further negotiations with Ajax for the 24-year-old after QPR's initial £5 million bid was rejected.
Sigthorsson has scored 24 times in 59 appearances for the Dutch club, who are looking for a fee closer to £10m, say the Standard.
In other news, Wolves boss Kenny Jackett says the door is still open for Keyin Doyle to return to the first-team. Doyle spent the latter part of last campaign on loan at Loftus Road.
Fulham have been strongly linked with the 27-year-old but the report suggests the club have failed to reach an agreement with Leeds owner Massimo Cellino.
Elsewhere, former Fulham defender Chris Baird has joined West Brom on a free transfer.
Baird spent last season at Reading and Burnley and has now moved to the Hawthorns on a one-year deal.