Thursday is the deadline for loan deals into the Football League, and Dorrans is wanted by up to half-a-dozen clubs.
It is believed that Nottingham Forest are leading the chase, but clubs such as Reading and Derby County are also in contention for his signature.
Dorrans has started just twice for the Baggies this season and has not featured in the league for them since early September.
Scotland international Dorrans is understood to want to secure first-team football, and a deal is now believed to be close.
A source close to Nottingham Forest confirmed to Sky Sports that they were hopeful of concluding a deal.