The 26-year-old Honduras international 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 the year.
Espinoza is a versatile player who can play in either defence or midfield and he impressed at this summer's Olympics with 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 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."