Martinez left the Latics earlier this month to take charge of Everton and Wigan have been searching for a replacement who can plot a promotion push in the Championship.
Whelan is close to concluding interviews and could even announce the new manager on Friday.
Ex-Bolton boss Owen Coyle, former England manager Steve McLaren and Manchester United first-team coach Rene Meulensteen have all been linked with the vacant position.
"I still have two more lads to see but I expect to announce something tomorrow," Whelan told BBC Sport.
"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."
The new man at the helm could lose a number of his big names as Whelan will not stand in the way of Martinez if he attempts to recruit his former players.
Forward Shaun Maloney has admitted he is unsure about his future, while striker Aroune Kone has been linked with a move back to the Premier League.