The former England coach McClaren and former Bolton Wanderers manager Coyle are among 15 candidates whom Whelan has interviewed for the position this week. Mike Phelan, who recently left his role as Manchester United's assistant manager, and the United coach René Meulensteen are also under consideration, though Whelan has indicated his preference for an out-of-work candidate.
"I expect to announce something," said the Wigan chairman. "I still have two more lads to see. I've seen some great lads, top managers, and it could be we have to speak to one or two of them again."
Whelan began his managerial search only after Martínez completed his move from the FA Cup winners to Everton on a four-year contract last Wednesday. The process was interrupted by a pre-arranged visit to Jersey over the weekend to parade the trophy that Wigan won three days before being relegated from the Premier League.
Whelan is keen to make a swift appointment as Wigan prepare for life in the Championship, a Europa League campaign and for the potential loss of several pivotal players.
Antolín Alcaraz, Maynor Figueroa and Franco Di Santo are all out of contract next month while James McCarthy and Arouna Koné are among those expected to preserve their Premier League status elsewhere. Alcaraz, the Paraguay international defender, may follow Martínez to Goodison Park but has offers from a number of European clubs.
Whelan has said Championship experience is not a prerequisite for the Wigan job, which may help McClaren as his only time at that level amounted to 13 games and 122 days with Nottingham Forest. The 52-year-old is available after leaving his second spell at FC Twente in February while Coyle, who won promotion to the Premier League with Burnley, has been out of work since being sacked by Bolton in October 2012.
"The total priority is for the manager to get us into the Premier League. If he can do that, then he's done his job and he'll be with us for a long time," said Whelan. "I don't like the thought of appointing someone just because they have specialised in the Championship though. That would be short term and I don't want to bring someone in like that. You need to have them with you for five or six years to be successful."
Wigan's chairman also conceded that an out-of-work candidate holds an obvious advantage. He said: "Some of the managers I've spoken to are under contract and that means compensation, which would not be ideal."
guardian.co.uk © Guardian News and Media Limited 2010
image: © illarterate