The statement continued: "We have already agreed a compensation package to Swansea City for Roberto and talks are ongoing between the clubs about the backroom staff.
"Once these issues have been resolved we will be able to unveil Roberto as new manager and get on with the job of preparing for next season. Thank you all for your patience."
Martinez wants assistant Graeme Jones and chief scout Kevin Reeves to move with him.
But Swansea chairman Huw Jenkins said they had been "left in limbo" over the issue, despite being as keen as Wigan to bring it to an end.
"Roberto and Wigan were fully aware we wanted compensation for them both, not just to buy out their contracts but for the vast amount of knowledge and experience they hold," he told the Swansea website.
"To lose our manager is bad enough but to think we would also lose our assistant manager and chief scout for nothing in the same compensation agreement as Roberto's is unfair and disrespectful to our football club and our fans.
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