Di Santo, Wigan's top scorer last season with seven goals, has hit the net three times in 2012/13 and made his senior international debut in November.
"His contract is not an issue. All our focus is on fulfilling Franco's potential from a footballing point of view," said Martinez.
"He's come a long, long way, but he still has a long way to go.
"I believe his potential is huge, he can be as good as he wants to be. But obviously he needs to be in the right environment to reach that full potential. And once he reaches that, he will be ready to challenge for anything.
"Remember, he's still a very young man. The level he showed at the end of last season and this season shows you that he has signs of getting there very quickly.
"We all share the same feeling. We want to work together for a longer period and it's just a matter of making it happen. Hopefully we will do that very soon.
"He knows he can trust the club in many ways because all we have done during his time here is help him with his development. There's a real trust in the relationship."