The Ghana winger, who spent last season on loan at Eredivisie side Vitesse, has been linked with Everton and Sunderland during the transfer window.
However, it is the Goodison Park club that appear to have won the race to sign the 22-year-old on a temporary basis, with Martinez revealing that a work permit is the only thing preventing the deal from being completed.
"Everything has been agreed with Christian - it's just a matter of finalising little details more with his work permit and personal situation," Martinez said.
"That will probably take a couple of days to get sorted but we have an agreement in principle to make the move as a loan deal until the end of the season."
Former Porto player Atsu, who scored five goals for Vitesse last term, should bring further quality to a side that finished fifth in the Premier League last term and has already added Romelu Lukaku, Muhamed Besic and Gareth Barry to their ranks pre-season.
Everton are still said to be keen to sign another striker, although Martinez indicated that the Merseyside club are happy to wait until the end of the window to make that acquisition.
"We'll take every day we have left in the window just to assess what we have in the squad and I'm happy with what we have," he added.
"I would say we will take right until the last moment."
