Martinez has been strongly linked with the vacant managerial positions at Stoke and Everton in recent weeks and he has already met with Latics chairman Dave Whelan to discuss his future.
The Spaniard is seeking assurances over Wigan's training facilities and youth development plans before committing to the club following their Premier League relegation. A second meeting this week is set to be crucial in deciding whether he will stay at the DW Stadium.
Former Crystal Palace defender Boyce, who captained the side to a memorable FA Cup success over Manchester City earlier this month, is keen for Martinez to stay and help them bounce right back to the Premier League at the first attempt.
"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.
"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.
"Fingers crossed we can keep most of our players together, keep our manager and hopefully challenge for the title next year."