The Latics' bid for West Brom's Peter Odemwingie was rejected on Friday out of hand by the Midlands club and it is believed that the Latics will return with a lightly improved offer for the 15 goal striker.
Speaking about the hope of new additions, Martinez said: "We are still looking for two players. I want to fulfil those roles with players who are already here, but it's only fair to the squad that we have enough numbers to face the demands of the Premier League, and we will do that.
"I don't know what players we are going to bring in, that is the reality, although I know exactly what we need from a character point of view.
"But having lost Cleverley and N'Zogbia, we are two bodies light.
"We need to bring in two players and that is where as a football club we are working extremely hard."
Also linked with the club is Manchester City's England international winger Shaun Wright-Phillips.
