Coleman has agreed to lead Sunderland who were relegated to England's second tier from the Premier League this year, the reports said.
They have been without a manager since sacking Simon Grayson last month after one win in their opening 16 league matches left them bottom of the standings.
Coleman, who became Wales manager in 2012, led his country to the semi-finals of Euro 2016, their first major tournament since 1958.
However, he was unable to guide them to next year's World Cup as they missed out on qualification from Europe's Group D last month.
The 47-year-old will return to club management having previously coached Fulham and Coventry City. He also had short spells abroad with Real Sociedad and AEL Athens.
(Reporting by Christian Radnedge, editing by Ed Osmond)
