Puel’s reign at Leicester ended with a heavy 4-1 home defeat to Crystal Palace on Saturday.
The Foxes have lost five of their last six Premier League games and currently sit 12th in the table.
That run of four consecutive home losses is their worst form for 19 years.
Puel replaced Craig Shakespeare as Leicester manager in October 2017, four months after being sacked by Southampton.
He led Leicester from the relegation zone to a ninth-place finish - only the club’s second top-10 Premier League finish since 2000.
During his one-season stint at Southampton, Puel led the team to the League Cup final and to eighth in the league. However, the team’s style of football and poor Europa League showing led to many fans calling for his head, which the Saints board gave them in the summer of 2017.