The Latics owner claimed to have received more than 50 applicants following Roberto Martinez’s departure for Everton, and he has met with around 10 of the frontrunners since Monday.
Whelan told BBC Sport that the process has almost reached completion, saying: "I still have two more lads to see but I expect to announce something tomorrow."
"I've seen some great lads, top managers and it could be we have to speak to one or two of them again, but I'd say it's likely we will make an announcement tomorrow."
Former Bolton boss Owen Coyle and ex-England manager Steve McClaren are thought to be the two favorites for the vacancy, with Manchester United first-team coach Rene Meulensteen and suspended Brighton boss Gus Poyet also in the running.
The new manager will have Europa League football to contend with at the DW Stadium following last season's FA Cup triumph, as well as the club's first promotion campaign in eight years.
The challenge to regain Wigan's Premier League status may be made even more daunting by the loss of some of the Latics' key players, with Shaun Maloney and Arouna Kone both linked with moves away.