Reports over the last couple of days had claimed that the former Manchester United, Liverpool and England midfielder had held talks with the Blackpool board about filling the manager's role at Bloomfield Road.
Speculation intensified further this afternoon when he was spotted at Portman Road to watch Blackpool take on Ipswich Town - a match that they lost 1-0 to the home side.
"There's going to be an announcement on Monday. It's going to be Paul Ince. The deal is very close to being done," Thompson told BBC Sport.
Ince has been out of work since he left Notts County in April 2011.