The Latics recently lost the services of Spaniard Ivan Ramis, who has been ruled out for the remainder of the season with a knee injury.
Despite having three days to secure a new defender, Martinez has insisted that he would like to get a deal done sooner rather than later.
"I don't really like going into the last day of the window without our signings done," he told reporters. "That's why we brought our two players in really early - Roger Espinoza and Angelo Henriquez.
"The injury to Ivan Ramis has put us in a position where we should be looking to add a defender."
Liverpool's Sebastian Coates was recently linked with a loan switch to the DW Stadium.