BBC Sport reports Wednesday are close to announcing Pulis as their new manager, just four days after the club sacked former boss Garry Monk.
Pulis, who has previously managed Stoke City, Crystal Palace and West Bromwich Albion in the Premier League, is expected to take over at Hillsborough after advanced talks over the past couple of days.
The final details, such as over Pulis's coaching team, are reportedly all that is left to be agreed.
The Welshman has not managed since leaving Middlesbrough at the end of the 2018-2019 season after the club failed to make it to the Championship play-offs.
In a cruel twist of fate for Monk, Pulis was also the man who replaced him when he was fired by Middlesbrough when the club were ninth in the Championship in 2017.