But Baggies head coach Roy Hodgson has ruled him out of the final Barclays Premier League clash of the season at Newcastle plus Scotland's programme of summer internationals.
Dorrans has been sidelined since sustaining the injury during training in early March and Hodgson said: "The good news is Graham might be able to join in training next week, which would be very good."
He added: "It will be good to get him back involved on the training pitch before he goes away for the summer break.
"But there is no chance he will play against Newcastle and he won't be involved with Scotland.
"It would be madness for him to play for Scotland because he has not played for months."
Hodgson will have skipper Chris Brunt and defender Steven Reid available for Saturday's home encounter with Everton.
Midfielder Brunt and Reid have missed the last two games against Aston Villa and Wolves with hamstring and calf problems respectively.
Source: PA
Source: PA