The move would mean new manager Jimmy Floyd Hasselbaink raiding his former club Burton Albion to sign the left-back.
Hasselbaink left Burton to move to QPR in November, and is gearing up to splash out in the transfer window to start shaping his team.
McCrory is a player he knows well and trusts, and his addition would be a good place to start strengthening, providing he is not worried about upsetting his former employers.
The 25-year-old hails from Ireland and is a former under-19 international for the Republic. He has been at Burton since 2012, when he signed from Dagenham and Redbridge, and began his career with Plymouth Argyle.
This season he has played 20 times in all competitions for Burton, but crucially for QPR, McCrory's contract is due to expire in June, helping their chances of convincing his club to cash in.