The Belgium international has been linked with a move away from Goodison Park this summer and has previously expressed his ambition to play in the Champions League.
The Toffees are under no financial pressure to sell Fellaini but a release clause in his contract means they would be powerless to stop a Champions League side from signing him should they match the release fee, believed to be in the region of £24million.
However, that clause expires on August 14, meaning clubs face a race against time if they are to complete a deal for the 25-year-old.
Martinez has refused to entertain the potential sale of Fellaini and demonstrated how important the midfielder is to his plans by handing him the captain's armband during Sunday's 2-1 friendly defeat to Austria Vienna.
The former Wigan boss says Fellaini is now a senior member of his squad and will have a key role to play the new campaign.
"Marouane is an international footballer and he's going to be involved, if all goes well, in a World Cup next year," he told the club's official website.
"He's had a fantastic impact in the Premier League and hopefully now is the time he can carry on showing his massive influence in the game for us.
"He's still a very young man but I am really looking forward to seeing Marouane working hard and making sure that he sets really good standards at this club. We have a very good group of senior players in our dressing room, and some players need that extra bit of responsibility.
"We have youngsters at the club and they need to get opportunities but the senior players at the club are massively important to start the season as strong as we can be."