Morrison is currently at Lazio, but he has barely featured for the Serie A club.
QPR are eager to bring the attacking midfielder back to England, but with time running out they need to agree a deal quickly.
As things stand, Rangers are rapidly trying to negotiate with Morrison, to give them a chance of signing the 23-year-old before the deadline closes.
Ian Holloway has already added Luke Freeman to his QPR squad this month, but he is eager to strengthen them going forward even more.
Morrison is certainly a natural talent, but his attitude has been called into question previously.
If Morrison does move to QPR, it will be his second spell at Loftus Road, after he spent time on loan at the London club earlier in his career.
Morrison scored six goals in 17 appearances for QPR during his first stint with Rangers.
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