Traore only joined Monaco from Anzhi Makhachkala earlier this month, but is set to move to the Premier League to gain further experience.
West Ham United had shown an interest in signing the 6ft 8in forward, but the Ivory Coast international is poised to move to Goodison Park for the rest of the season.
Martinez has been keen to bring in attacking reinforcements after losing Arouna Kone to injury and selling Nikica Jelavic to Hull City.
"Lacina is a player who I really like and is someone who would fit in really well in the role we want the player to come in," said Martinez after a medical allayed any concerns over a hamstring injury.
"There are a couple of hurdles that we need to get over; the work permit is something we need to look into.
"If we can get through that he will be a player we will be very keen to add to the squad.
"He had a recent soft tissue problem but it is not too bad. He is a few days away from being fully fit and we were quite happy with the medical.
"Every work permit is difficult. We have a very strong case of showing why we need Lacina with us.
"He is a very talented footballer. He is only 23 and has already had a couple of moves (totalling) nearly £30million but every work permit is a difficult one and we will try our best."
Meanwhile, Sam Allardyce insists no-one at West Ham is to blame for the signing of Traore slipping through their grasp.
West Ham had applied for a work permit for Traore before Everton stepped in, but Allardyce does not feel the Hammers missed out due to dragging their heels.
"To apportion blame at the end can end up in all shapes and forms," he said.
"All I'm saying is that we could have done no more than we did by trying to secure a player of this size, quality and talent. In the end we had a long process of going as far as the work permit.
"It wasn't Monaco and it wasn't us, it was all down to the player's agent. That is who he listened to. That is what happens in today's modern-day game."