The former Wigan boss has already signed four players this summer, raiding the Latics for Aroune Kone and Antolin Alcaraz, while also taking Joel Robles from Atletico Madrid and completing a loan move for Barcelona's Gerard Deulofleu.
The Toffees have been strongly linked with a season-long loan move for England international Gareth Barry, who has entered the final year of his contract at Manchester City.
Martinez insists he has not given up his efforts to further strengthen as he seeks to make his mark at his new club.
He told the Liverpool Echo: "It's not about being hopeful, it's about working hard and trying to identify maybe one player if we could. But he has to be the right character to adapt to what we want to do at Everton.
"It's not that we are desperate in terms of numbers - that is not the case. We've got good numbers in the squad but we need maybe to have a little bit of help in an area.
"As I say, we will work extremely hard in that respect (to find someone)."