However the club are "confident" the wrangle with Swansea over compensation for the Spaniard's backroom staff will be resolved next week.
Martinez, 35, arrived at the ground on Thursday in anticipation of being presented to the media. However, instead he was not called.
It is understood he has agreed a three-year deal to succeed Steve Bruce, now with Sunderland, at the DW Stadium.
The club have now released a statement to bring supporters up to speed with the situation.
It read: "Wigan hoped to unveil Roberto Martinez as new manager yesterday. But due to Swansea City wanting further compensation for Roberto's backroom team it was felt that delaying the announcement of Martinez was the only option.
"Wigan would like to apologise to the media at yesterday's event and to the supporters for the delay.
"The club would like to stress that talks with Roberto have been extremely positive and personal terms have been agreed.
"We are confident to resolve the issue by early next week. 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 is keen to take his assistant Graeme Jones and chief scout Kevin Reeves with him.