The Scotland international was linked with Championship counterparts Nottingham Forest earlier this week.
Mackie is under contract with Rangers for another two years and the club is thought to have accepted a £1.5m offer from Forest.
QPR boss Harry Redknapp is on the lookout for a new striker, although his attempts to lure Gary Hooper from Celtic appear to have failed - with Norwich City now expected to sign the Englishman.
An R's statement read: "Jamie Mackie has today (Thursday) submitted a transfer request, which the club have reluctantly accepted.
"The 27-year-old has informed the club of his desire to leave, having found first-team opportunities limited at Loftus Road in the last six months.
"As previously stated, no player will leave QPR unless the club's valuation is met.
"The club will be making no further comment at this time."
Mackie has made 94 competitive appearances for the Championship club, scoring 18 times since moving from Plymouth Argyle for £145,000 in May 2010.