Martinez said: "We're working really hard to try to make it happen and we're looking forward to seeing if we can get that one done successfully."
Espinoza is a versatile player who can play in either defence or midfield and he impressed at this summer's Olympics with Honduras, in particular in his performance against Brazil in the quarter-finals.
Martiniez added: "There are a few steps: there is the work permit, there are certain aspects we need to fulfil in the paperwork but Roger is a player that we've been following for a long, long time.
"We've seen him enjoying his football in the Olympic Games recently with Honduras, and in the World Cup as well he's been an important part of that group of players with ( Wigan defender) Maynor Figueroa. He would be a real asset for us.
"But until January 1 it's something we can't do any more than wait on and make sure we prepare ourselves for the steps we've got ahead to make him a Wigan Athletic player."
Reinforcements cannot come quickly enough for Martinez, who is set to be without eight players for Saturday's meeting with QPR through a combination of injury and suspension.