The Toffees have already signed youngsters Shani Tarashaj and Matthew Foulds for the long term but Martinez is now looking for recruits to make an impact during the second half of the season.
Dynamo Kiev striker Andriy Yarmolenko is a player Everton have been consistently linked with over several windows.
Martinez claimed he did not know the Ukrainian's agent was at Goodison Park for the FA Cup win over Dagenham on Saturday but confirmed he has irons in the fire.
The Everton manager said: "We've been working really, really hard to get some business (done) really early
Shani Tarashaj was our target number one in terms of doing it quickly
"We've got a couple of situations that could happen
The shape of the squad is going to be determined in the last week of the window and we want the squad to be stronger than it is now."
Martinez is also hoping to offload a couple of players on the fringes of the squad.
Winger Aiden McGeady was left out against Dagenham because three clubs, two domestic and one from abroad, have shown an interest in taking him on loan.
Midfielder Darron Gibson could leave on similar terms while forward Steven Naismith has been the subject of enquiries from Norwich and another Premier League club.
Martinez said: "We're going to work together with Aiden and his representative and we're going to make the right call
There's been three enquiries and it's going to be over the next couple of weeks that we're going to make the final decision.
"It would be a loan until the end of the season and (he and Gibson) would be returning and competing strongly in pre-season in view of the next campaign."
Everton return to Premier League action on Wednesday with a trip to the Etihad Stadium to face Manchester City.
Martinez is looking for a repeat of the first leg of the Capital One Cup semi-final last week, when they produced one of their best displays of the season to win 2-1.
That avenged a 2-0 home defeat in the league in August, with the second leg of the cup clash to come in a fortnight.
Martinez said: "The previous time we faced Manchester City in August at Goodison, it was a very similar game
Both teams had chances but ultimately I don't think we showed enough belief that we could win the game
"It was completely different in the League Cup semi-final
There was a complete focus on what we wanted to do and the belief that we were going to do that
"The mentality has grown
That psychological aspect that we showed is exactly what we need
"Any time you face the same team, it has an effect
We're looking to go to the Etihad and face the team with the best home record in the league.
"We feel very confident away from home, we've got a really good record
I can see a really tight game and the familiarity between the two sides can only help to make it a more interesting encounter if anything."
Romelu Lukaku will lead the line after recovering from an ankle problem and Ramiro Funes Mori is fit despite needing 10 stitches in a head wound sustained against Dagenham.
Tom Cleverley is a doubt because of an ankle problem while Seamus Coleman's calf injury will keep him out for another two weeks or so.
Martinez confirmed, meanwhile, that Tim Howard will return in goal despite a shaky season and Joel Robles' good form in the cups.
The Spaniard said: "Joel Robles has been terrific but Tim brings a unique experience and know-how.
"Of course you get good moments and bad moments like any player but we appreciate what Tim Howard brings on top of being in between the sticks."
Source : PA