The former Norwich City and West Bromich Albion ace has impressed since moving to Glasgow, but has missed his side's last two matches after picking up the injury against Kilmarnock.
The report claims the 30-year-old will now see a specialist over the injury, and it could see him miss Rangers' double-header against Derek McInnes' Aberdeen, with the two sides going face to face on November 29 and December 3.
With Dorrans definitely ruled out of Saturday's clash against Hamilton and next weekend's trip to Dundee, Murty has a decision to make when replacing the Scotland international.
Jason Holt has come into the side to replace Dorrans, but interim boss Murty should give his side more attacking bite by handing Mexico international Carlos Pena a chance to redeem himself.
The 27-year-old powerhouse is yet to prove his £2million transfer fee at Ibrox, making just nine appearances in all competitions with question marks still being raised over his fitness.
Costing the club as much as that, Rangers must give Pena more of a regular chance to prove to fans and the Gers hierarchy that he is worth the expense, and he can do that by starting over Holt on Saturday.
During his nine appearances, Pena has scored an impressive four goals. His attacking tenacity and powerful demeanour from deep would provide Rangers with the necessary ammunition to dispose of Hamilton this weekend.