Al-Habsi has been the number one in recent weeks after displacing Kirkland earlier in the season. However Saturday's game with his parent club Bolton meant the Oman international goalkeeper was forced to watch from the stands.
This gave Kirkland the chance to come back into the side and prove himself capable of holding on to the number one spot.
However Al-Habsi came back in for the mid-week Carling Cup victory against Martinez' former club, Swansea City, leaving the situation unclear.
Roberto Martinez spoke this week about the situation, and he was unwilling to offer any thoughts on who was his number one. Instead, the Latics boss spoke only of his head ache regarding the problem.
He said: "The situation hasn't changed at all. I know there has been plenty of talk in the media. We are extremely proud at the club to have three goalkeepers challenging for the No.1 jersey and that brings a great competition.
"We're working extremely hard to build a competitive squad and the situation is no different with the 'keepers.
"Al Habsi has been playing very well, while Kirkland has been No.1 for many years and he has the respect from everyone which he has rightfully earned and we've also got Mike Pollitt.
"Kirkland played really well against Bolton at the weekend and showed that he is ready, while Ali has been playing extremely well at the moment and has shown he is patient.
"It is the sign of a very good squad when you have players such as Ali, Chris and Mike competing for the one position."