And Martinez believes Espinoza will prove a huge asset to the Latics.
The 26-year-old has long been linked with a move to the DW Stadium and is set to swap Major League Soccer for the Barclays Premier League when his MLS contract expires at the end of this month.
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.
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.
"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.
Gary Caldwell must serve a one-match ban after picking up his fifth yellow card of the season while fellow defender Figueroa also sits out the key clash.
The Honduras international was sent off in the 12th minute of Monday's 3-0 defeat by Newcastle at St James' Park for a tackle on Papiss Cisse.
Figueroa was deemed to have denied the striker a clear goalscoring opportunity, and the Football Association upheld the decision this week, turning down Wigan's appeal.
The Latics felt their defender was doubly harshly treated given the challenge was shoulder to shoulder and the ball rolled through to keeper Ali Al Habsi.
Martinez said: "I just felt that we were very unfortunate with the decision on the day but, from Maynor Figueroa's point of view, he was devastated.
"All he did was challenge for a ball that he was entitled to and from then on he gets a penalty, we concede from it, and then he gets sent off. That's punishment enough in my eyes, but then he has to carry a ban for the next game.
"So we had to do everything we could to try to give Maynor a little bit of fairness. Unfortunately that hasn't been the case and in football you just move on. We accept the decision and we'll get ready for Saturday now."
Martinez believes the interpretation of the rule is seeing players punished too harshly for tackles and has called on the footballing authorities to look at it.
The Spaniard said: "The rule is clear in terms of if it's a clear goalscoring opportunity and you're the last man, it's a red card.
"Then obviously there's the interpretation of the referee, and we don't make it easy for referees because there's so much you have to take in in a split second. But I think bringing a bit of common sense into that rule would be important.
"I think the authorities should look into it. The last thing you want is to be punished so much for what could be an innocuous challenge or a fair challenge to compete for the ball. Football is a contact sport and will always be."
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