The midfielder, 18, joined January from Sivasspor for 4m, but suffered an adductor injury two weeks into his Bees career.
Konak was to spend the remainder of the season with Brentford B, though the door would be open to the first team should he impress.
Advertisement
Advertisement
Turkey U21 international is now working towards a playing return.
And the London Evening Standard says he has been training individually for the past fortnight and there's confidence he's now ready to join full-scale senior training.