Wigan's current number one is Ali Al-Habsi who is only on loan from Bolton Wanderers and Martinez wants to secure someone permanently with Chris Kirkland failing to prove his long-term fitness.
Meanwhile, Wallace, would come in and add competition for the left-back position, currently occupied by Maynor Figueroa who has also been linked with a move away from the DW Stadium.
The Latics are expected to send scouts to watch the 23-year-old face Celtic tonight.
Boss Roberto Martinez is a long-time admirer of Wallace and has continued to monitor his progress since he returned from injury.
The Spaniard was keen to see how he recovered from cruciate ligament damage suffered while playing for Scotland against Liechtenstein back in September and he has been highly impressed.
Martinez had spies in the stand for Hearts' stunning win over Rangers on Saturday and is now weighing up a bid before the end of this transfer window.
Wigan current first-choice left-back Maynor Figueroa has been linked with moves away from the DW Stadium and Martinez sees Wallace, whose Hearts deal runs until 2012, as competition for the Honduran or an ideal replacement.
Manager Jim Jefferies is keen not to lose any of his best players this month due to the club's proximity to the Old Firm in the SPL table.
He said: "If an offer comes in for one of our players in the current transfer window that can't be turned down I'll have to discuss the situation with the owner.
"I'm nervous about that possibility but it's part and parcel of football.
"I really hope that doesn't happen so from now until the transfer window closes I'll try not to answer my phone."
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