The Gunners custodian, a £6 million signing from Ipswich Town, has missed the last eight matches after aggravating a knee injury during the Champions League defeat to Deportivo La Coruna.
But the England star, 24, is poised to be between the sticks for the reserve game with Peterborough on Thursday and if he comes through the 90 minutes unscathed a possible starting place against The Reds could be on the cards.
England Under-21 keeper Stuart Taylor has been keeping goal in the absence of Wright, and the injured David Seaman, and has not put a foot wrong.
However, Gunners coach Arsene Wenger may opt to rest Taylor and introduce the more experienced Wright for the six-pointer crunch tie at Anfield.
