Whelan to meet Wigan candidates
Wigan, who were relegated from the Premier League despite winning the FA Cup last season, are looking for a new head coach after Martinez agreed to join Everton earlier this week.
"I've got about 10 or 12 to interview over the next few days and hope to make an announcement by next weekend," Whelan told Sky Sports News.
"There were more than 50 applications. I can't interview all of them, but I thank them for applying."
Figures linked with the vacancy include Brighton and Hove Albion manager Gus Poyet and Mike Phelan and Rene Meulensteen, both of whom worked as assistants to outgoing manager Alex Ferguson at Manchester United.
Whelan would not be drawn on the candidates' identities, however.
"I'm talking to a lot of great managers. Hopefully I can choose the right one, and that's not easy," he said.
"They all need that bit of luck to succeed. We've only one ambition and that's to get back in the Premier League."