As exclusively revealed by Goal, Arsenal activated the Belgian's release clause in June but have not agreed personal terms, while the left-back has reportedly been the subject of an offer from Manchester United, now managed by former Toffees boss David Moyes.
Asked by reporters if there were new approaches, Martinez replied: "Not at all, and I know that obviously that's not something that you want to hear.
"But, clearly, what has been in the last two or three weeks is everyone focused to try to fight for that starting spot at the beginning of the season. The competitive level in this group is quite impressive.
|16/1||Everton are 16/1 with William Hill to finish in the Premier League top four
"If we get clubs talking about our players, I'll take that as a compliment because, our players, they've been impressing and they've been doing very very well but we're in a great position financially, we're really really strong and what we want is to start the season with the best possible squad that we have and for that we have to work extremely hard.
"The last concern that I have is what the other teams do and what I've been really impressed [with] is the togetherness of this group and the professionalism of this group is something that you get straight away.
"And I said it before when I arrived at Goodison. I saw the passion of the fans and the feeling of the football club and believe me I can see that through the players in every training session and it pleases me. It makes me proud.
Questioned on whether he could keep his squad together, the Spaniard answered: "That's something that you should never ask to a manager because unfortunately the modern game doesn't allow managers to do that in terms of having that control.
"What I'm very, very excited [about] is that the squad is very, very strong. There are always good youngsters, the club is producing youngsters that I feel are going to come to the first team and give a real good hand to the players that we've got there."