Feyenoord coach Slot will replace Jurgen Klopp at the end of the season.
"I would have given more thorough consideration to a coach like Thomas Tuchel, who took on and beat Pep Guardiola in the ultimate test - a Champions League final," Carragher wrote in the Telegraph.
Advertisement
Advertisement
"Tuchel followed Klopp at Mainz and Borussia Dortmund and did well.
"It has not worked out at Bayern Munich this season, but you only have to look at Carlo Ancelotti and Unai Emery to recognise how top coaches recover from setbacks."