The Latics chairman claims he is set to interview "10 or 12" top coaches this week, with the intention to appoint one of them as soon as possible
The Spanish manager officially succeeded David Moyes as Everton boss on Wednesday, leaving the Wigan job vacant as the club prepares for life in the Championship.
And Whelan recognises the difficulty he has in appointing the right successor, but is more than happy with the applicants he has to choose from.
"I'm talking to a lot of great managers," Whelan told Sky Sports. "Hopefully I can choose the right one - and that's not easy.
"They all need that bit of luck to succeed. We've only one ambition and that's to get back in the Premier League."
Former Manchester United assistant manager Mike Phelan has been linked with the post as have Owen Coyle and Gus Poyet and Whelan is hoping he can have a new man in place soon.
"I've got about 10 or 12 to interview over the next few days and hope to make an announcement by next weekend," he added.
"There were more than 50 applications. I can't interview all of them - but I thank them for applying."