The new Latics chief, who stepped into the hot-seat following Paul Jewell's departure at the end of last season, has been a busy man in the transfer market so far this summer.
Hutchings has already recruited Titus Bramble, Antoine Sibierski and Mario Melchiot, as well as Helsingborg defender Andreas Granqvist.
But he sees playmaker Koumas and a new striker as the final pieces in his jigsaw for next season's Premier League campaign.
The Baggies have already rejected Wigan's £4million bid for the Wales international, and are believed to want around £5.5million for him.
But Latics are not prepared to go any higher than £5million for the 27-year-old, who is also wanted by Everton, Fulham and Reading.
If Albion agree to that valuation, the Cottagers and Royals are likely to match Latics' offer, and it could then boil down to personal terms and who Koumas would most like to play for.
Lawrie Sanchez's long-ball tactics would be unlikely to appeal to Koumas, while Steve Coppell sees him as the man to replace Steve Sidwell as the creative force in the Royals' midfield engineroom.