The 26-year-old Honduras international caught the eye with some sparkling displays during the London 2012 Olympics and has been linked with a move to the DW Stadium in recent weeks.
Espinoza, who can play in defence and midfield, is expected to pen a two-and-a-half year deal with the Latics.
And Wigan boss Martínez revealed a deal was close on Thursday.
“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,” said Martínez.
“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 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.”
ENHANCED ODDS: Get 7/1 on Man Utd to beat Swansea