While Arsenal has thus far failed to agree terms with the Belgian, and Manchester United remain linked with the left back, the Everton boss says that the situation is unchanged.
Arsenal reportedly activated Fellaini's release clause in June but has not agreed to personal terms, while Baines 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, though, 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.
"And I wouldn't want to stop the speculation, I do think that the speculation is healthy. The speculation of trying to be as good as we can before the window closes in our football club will always be the case.
"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."
As for whether Martinez could keep his squad together, the Spaniard answered bluntly, saying that while he is excited about the squad he has, the current era takes away control from the club and manager
"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," Martinez said. "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."