The Merseyside club were granted a work permit for the Ivory Coast international on Tuesday ahead of a proposed loan move for the rest of the season.
Martinez expects Everton to find out on Thursday if the deal will go through and is optimistic an agreement can be reached with the wealthy French club.
"We're still working on it, there is nothing to announce as yet. The work permit was successful, there a few other issues to get through but there is nothing to announce," he told reporters.
When asked if Falcao's injury could scupper the deal, the Spaniard added: "We hope that's not something that should affect the decision to allow Lacina to go out on loan.
"At the moment the deal is not complete, so it's difficult for me to comment but it's something we should find out quite quickly in the next few hours."
If Martinez does get his man, the boss expects the signing of Traore to be his last before the transfer window shuts next week.
He said: "That will probably be it, the main two targets was a striker and Aiden McGeady [who signed from Spartak Moscow on January 11]."