As exclusively revealed by Goal.com last week, McCarthy was the subject of an enquiry from the Gunners earlier in the transfer window.
But, when asked whether there was any truth in the rumours that McCarthy might be set to leave, Martinez told reporters: "No. As you know, at this moment the last thing we want is to lose players. We are not going to lose players.
"We are not a football club that have got big amounts of money to spend but what we haven't got is debts.
"We made a profit of £4 million this year and that means that we can re-invest and we can look internally to try to be as strong as we can be.
“We are not going to lose any players, if anything we are going to add some.”
Having witnessed his side fall to a 3-2 defeat to Sunderland on Saturday afternoon, the Spaniard also lamented the defensive injury crisis currently affecting the Latics.
He added: “With the injury of Ivan Ramis on top of the injury to Antolin Alcaraz, we haven't got a large enough squad to lose two or three players in the same position to cope with it.
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“The reality has been that we haven't been able to defend the same way we did in the last nine games of last season and since the Spurs game we have never been able to play the same team.
“That is something that isn't an excuse, that's a reason and I need to find a solution.”
But Martinez did underline his desire to bolster his ranks following the news that centre-back Ivan Ramis has been sidelined for the rest of the seasonn.
”Yes, we do. Generally, I think it is a good moment for us to rectify that," said the Latics boss when quizzed on his intentions for the window.
“It is difficult for a foreign player to come in in January to make an impact and pick up the tempo of this league straight away. So I will be looking more for players that have had that experience.”