The transfer talk involving his side may be focused on the possible departure of defender John Stones to Chelsea but the Toffees remain keen to strengthen their squad.
Everton have been linked with River Plate defender Funes Mori during the transfer window and the player was seen watching from the stands with a club scarf in his hand as Martinez’s side lost 2-0 at home to Manchester City.
“Ramiro was in the building yesterday (Thursday), we hope that we’re going to complete the deal some time today,” said Martinez.
“International clearance could take a few days. We’re very excited about having him.”
Forward Rodriguez, who plays for River Plate Montevideo, is also on his way to Goodison Park, according to Martinez, as the manager attempts to build a team capable of improving on last season’s 11th place Premier League finish.
“Leandro is going to be announced as well later today,” added Martinez.
“Leandro is one of the young players we identified to give them a path and allow them to develop in our system.
“We’re very excited, he’s someone who can produce a goal out of nothing, hard working with a really strong combination.”