The 39-year-old Spaniard, who is Everton's first-choice candidate to succeed David Moyes at Goodison Park, has held talks with Wigan chairman Dave Whelan and is set to make a decision regarding his future.
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"Everyone at Wigan is hoping he is going to stay," Boyce told Sky Sports.
"He's done such a fantastic job since he has been there. The football that we play and the entertainment value has been excellent.
"As a coach we learn so many things from him. People can say we are fighting at the bottom of the table but for the size of a club like Wigan to survive this long is a fantastic achievement and to win the cup is a dream come true."
Boyce has backed Martinez to eventually move to a high-profile club but believes the Spaniard could lead Wigan's charge for the Championship title next term.
"I know he is an ambitious manager and he will manage one of the better teams but from my point of view I hope he stays because I think next year will be a really, really good season for us," he added.
"Fingers crossed we can keep most of our players together, keep our manager and hopefully challenge for the title next year."