"We have a verbal agreement but nothing's on paper yet," Leafs interim GM Cliff Fetcher told The Canadian Press on Sunday.
"It isn't a contract until it's signed by the parties. And that won't happen for a couple of days."
An announcement could come as early as Tuesday.
The 53-year-old Wilson was fired last month by the San Jose Sharks after his team lost in the second round to the Dallas Stars. It was the fourth straight season Wilson had led the Sharks to the playoffs in his five seasons there.
Wilson, who grew up in Fort Erie, Ont., holds the Sharks coaching records for wins (206), winning percentage (.535) and post-season games coached (52). In 2004, he coached the Sharks to the Western Conference final.
He has a 518-446-127 career record during stints with the Anaheim Ducks, Washington Capitals and the Sharks. He also coached the U.S. to the 1996 World Cup of Hockey title, beating over Canada in the final, and also led the Caps to the 1998 Stanley Cup final.
Wilson would succeed Paul Maurice, who was fired May 7 after missing the playoffs in back-to-back seasons.