The 26-year-old Sporting Kansas City player is set to swap Major League Soccer for the Premier League when his contract expires at the end of the year.
Espinoza, who can play in either defence or midfield, impressed Martinez with his performances during this summer's Olympics.
The Wigan boss 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 we can't do anymore than wait and make sure we prepare ourselves for the steps we've got ahead to make him a Wigan Athletic player."
Espinoza's Kansas City team-mate Matt Besler could also be heading across the Atlantic, the MLS defender of the year is understood to have been offered trials in the Premier League.
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