It's understood the two clubs have finally reached agreement over a player who has been pursued by Canaries boss Chris Hughton for some time.
The news may come as a blow to QPR boss Harry Redknapp, who thought he was in the driving seat to capture the prolific 25-year-old frontman after Rangers too had a bid accepted.
Hughton, who is currently in the United States with his players preparing for the new season, will now hope the club can agree personal terms and that Hooper will complete a medical before sealing the deal.
Asked about the former Scunthorpe striker in the wake of a 1-0 defeat by Portland Timbers during the early hours of this morning, Hughton told the Eastern Daily Press: "We are still working very hard.
"It is very difficult for me with the eight-hour time difference, but even with the conversations I am having with the chief scout it is trying to find the right times. Nothing imminent, but we are still working."
However, things appear to have moved on rapidly since then amid speculation that Hooper could even undergo a medical later today.
QPR appeared to have made significant progress when their bid, understood to be in the region of £5million, was accepted, but that simply prompted Norwich to step up their interest.
Hughton initially tried to sign the player in January, although Celtic boss Neil Lennon has repeatedly spoken of his hope that he would remain at Parkhead, where he has 12 months remaining on his contract.
Speaking in Dublin last month, Lennon said: "There are no offers in and one of my priorities will be to try to keep Gary at the club."
Hooper was used as a substitute in Tuesday's Champions League qualifier victory over Cliftonville, but his days in Glasgow appear to be numbered.
The Essex-born marksman began his Football League career at Southend, but rose to prominence after a £175,000 switch to Scunthorpe in July 2008.
His form at Glanford Park won him a £2.4million transfer to Celtic two years later and he has not disappointed, finishing as the Bhoys leading scorer in each of the last three seasons.