The Polish midfielder has failed to settle in west London while also failing to impress new boss Ian Holloway.
Signed by Jimmy Floyd Hasselbaink in the summer, Borysiuk has made only 12 appearances, three bookings, no goals and an injury that delayed his debut.
In contrast, fellow countryman Pawel Wszolek has got into his stride under Ollie with praised heaped on the Hellas Verona winger for his energy and drive.
Rangers will listen to offers for Borysiuk, and set to replace him is midfielder Sean Goss from Manchester United, with a £500,000 agreed.
Goss, 21, joined United from Exeter City in 2012 but never made a first-team appearance at Old Trafford, although he drew comparisons with Michael Carrick over his passing when he was part of the United U18s.
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