The former Chelsea player has been a key member of the squad under Martinez, but the unresolved contract negotiations have even led to the Argentine being dropped.
However, Martinez told reporters that Di Santo will not be sold next month, despite reports linking him with a move to Liverpool.
Martinez said: “We can’t afford to lose Franco or anyone else just now. We are working with Franco, but right now results are vital.
“Franco had an incredible experience with us last season. He was unbelievable in the last nine games.
“He is a very important player for the squad.”
The 23-year-old moved to the Latics two years ago, signing for a fee of £4 million. This season he has scored three goals in 18 League appearances, of which he has started 14 and come on a substitute four times, testing the opposing goalkeeper with 34 shots so far.