Morrison, 22, agreed a move to Serie A side Lazio earlier this year after being released from his contract by West Ham, although he could not link up with the club until this summer.
Due to this ruling, he has yet to play for the club, and although he is training with them, he is believed to be keen on securing a return to England.
The former Manchester United youngster spent a 15-game spell with the R’s in the 2013/14 season, scoring six goals and helping Harry Redknapp’s side reach the play-off final - which they went on to win.
He also spent spells on loan at Cardiff and Birmingham after falling out with the management at the Boleyn Ground, and the report states that he is closing in on a move back to London.
His representatives are believed to be close to cancelling his contract with Lazio, and he is expected to return to Loftus Road in the coming days.
There are some reservations about Morrison from head coach Chris Ramsey and director of football Les Ferdinand, but having seem him impress so much during his last stay with the club, they see the young midfielder as a vital cog in their plans to rebuild the club in search of an immediate promotion back to the Premier League.