With many media outlets claiming that Wigan boss Steve Bruce, who is a Geordie, will become the next manager of Sunderland FC after being given permission to speak to them by Wigan Chairman Dave Wheland, there has been a lot of speculation linking Martinez to the Wigan job.
If the Swansea job were to become vacant, then many Swansea supporters want Swansea born and bred Coleman as their next manager.
The Sky Blues boss received raptuous applause at the Liberty Stadium from all sides of the ground when City drew 0-0 there on Boxing Day and got plenty of cheers when Swansea played at the Ricoh Arena.
The good news is that Swansea will not let Martinez go without a fight and their Chairman Huw Jenkins told the BBC: "I wouldn't let anyone speak to Roberto. "I would speak to Roberto on any issues that come in. We've a good open relationship, and if and when any approach was made I would discuss that matter with him fully.
"I firmly believe it's the make-up of his personality that when he signs a contract he will see that through.
"We've a man in Roberto who's fully committed to his job, and under contract for a few years.
"I don't think he wants to get involved every year in the manager merry-go-round that exists in our game and that ruins most football teams.
"There's far more about him as a man than to get involved in that."
"Wigan have got more funds available because of the Premier League handouts, so they would probably pay more wages and the manager would have a bigger budget to work with.
"But looking at it from my point of view, I don't see it as a step up at all.
"We've far more potential for a greater support than Wigan would ever have.
"I firmly believe Roberto should be looking to the top six in the Premier League, or the top teams around the world if and when he decides to move on. "He's young enough and he's got plenty of time on his side to do that."