Cardiff midfielder Aron Gunnarsson has signed a new two-year contract extension with the club.
Celtic have signed defender Dedryck Boyata from Manchester City on a four-year contract.
Bodde, signed by Martinez for Swansea in 2007, has been without a club since he was released by the Welsh outfit over the summer.
The 30-year-old has been blighted by knee problems and last played first-team football in the 2009/10 season.
He has been training with his first club ADO Den Haag back in his homeland and will now be reunited at Wigan with Martinez, who was giving little away about the prospect of the player signing a deal at the DW Stadium.
"It is just having him training, for him to see how he feels and how the knee reacts," said Martinez, speaking this morning ahead of Saturday's Barclays Premier League match at Norwich.
"It is just to see how he gets back into shape, nothing else.
"I'm sure he wants to work in a group. He has been working with ADO Den Haag for a few months and I think it will be great just to see where he is and how his situation is after a long spell with injuries."
Asked if it was too early to say about the possibility of Bodde joining Wigan, Martinez, who left Swansea to take charge at Athletic in 2009, said: "Yes. It is going to be great to see him. I always said he was the best player in his generation and it has been a real shame that out of the players that started something special at Swansea, he is the only one who has not played in the Premier League (Swansea won promotion to the top flight in 2011).
"That is a real shame and I hope that one day he can get that reward. But that is a long way off.
"It is important that he gets himself fully fit and sees how he feels. We are going to try to help him in that respect and see if he is fully recovered."
Meanwhile, Martinez has said there has been no firm interest from other clubs in James McCarthy and indicated that he expects the midfielder to stay with Wigan for the rest of the season.
The manager claimed after McCarthy's two-goal performance in last weekend's 2-2 draw with QPR that, while he was keen to keep the Republic of Ireland international, he had "the potential to play anywhere in the world", adding that "whenever he's ready we'll never stop him."
But Martinez has stressed the 22-year-old was still developing and suggested the distraction of transfer talk was the last thing McCarthy needs right now.
"We will always feel really pleased with compliments towards our players," the Spaniard said.
"But James McCarthy is a young man, at 22 he is still developing.
"One day he will be challenging to win titles and to be in the highest position in the game, there is no two ways about it.
"But he is still developing and the performance that he had on Saturday shows that he is developing in the right way.
"He knows that and he knows as well that it is an important time as well for his role with the national team.
"The last thing he needs now is to be distracted from his good work and the way he is developing."