Latics chief executive Jonathan Jackson is keen to retain the services of the manager, and revealed talks involving Martinez and chairman Dave Whelan will take place in the near future.
"Clearly Roberto will be linked with other jobs because of how well he's done here, but we all want him to stay," Jackson told the Wigan Evening Post.
"Roberto has done fantastically well for this football club and we'd love him to remain here for many years.
"We've all been fully focused on what was going on at the end of the season, and ensuring we remained in the Premier League.
"Now we can look forward, and that (Martinez's future) will be one of the main topics on our agenda. It will be something we'll be looking at over the next month or so."