King has scored 11 goals this season for the Hornets as they push for an immediate return to the top flight where he netted four in 14 games last season in an injury-hit campaign.
"We've shown an interest and it's ongoing," added Latics assistant boss Eric Black.
A move to Fulham broke down last week due to medical concerns, and Black concedes it is a matter that will be addressed should they come close to signing King.
"You are obviously concerned with something like that," added Black.
"But if something did happen then we would obviously have to satisfy ourselves that it wasn't an ongoing problem and wouldn't be a problem in the future.
"Hopefully if we do get him then he could contribute between now and the end of the season."