The 28 year old spent much of last season on the bench for Stoke as Tony Pulis favoured Ricardo Fuller as a lone front man.
The arrival of Jones from Sunderland would now appear to signal the end of Tuncay's stay at the Britannia Stadium.
With 22 goals in 72 appearances for the Turkish national team, and the ability to play on either flank, or up front, Tuncay would appear to be a perfect signing to fit in the Martinez style of play.
The Latics boss was also not keeping secret his desire to sign at least one more forward player before the close of the transfer window.
He told the Wigan Evening Post: “We are trying to bring two or maybe three players in before the end of the transfer window.
“It’s a long time to go until January, when you can next do something about your squad. I just feel that, even though I am pleased with the quality we have here, we need to make sure we have good strength in depth and numbers.
“It is hard at this stage of the season, but we have been following a number of players, working extremely hard, and hopefully something will happen.
“If they come off, then great. If not, at least all the major targets we were after are already at the football club – and that is great reward for the amount of work we have put in.
“We might be a little bit thin up front, and we are looking to do something this month. I am not just talking about bringing in cover, either. The players we are looking at have to be able to start straightaway.”