Cleverley and Besic have both been out injured for a considerable period of time, but they are nearing returns now.
And Martinez says that both are keen to be back involved as soon as possible, which will be important for his team in the future.
“It’s really important for us to have players like Mo Besic and Tom Cleverley desperate to be on the pitch again and pushing for their places," he explained.
Cleverley and Besic’s returns will considerably enhance the quality of Everton’s midfield options, and should further strengthen their squad.
Cleverley has not played for the Toffees since August, while Besic has been out since September.
The Toffees have made a good start to their season, but they have a number of first team players making their way off the treatment table – with Leighton Baines also close to a return.
It means that optimism is high at Goodison Park, with the side currently sitting in seventh place in the Premier League table.
Everton’s next match comes against Bournemouth, but Martinez has suggested to the club’s official website that fixture could still come too soon for Besic and Cleverley to start.