According to German media reports on Tuesday, the club may name Dutch Jos Luhukay as their new coach.
Luhukay, the former coach of Hertha Berlin, will succeed Stuttgart coach Jurgen Krammy, whose contract expired with the fall of the club.
The board of directors of the team has taken this decision and is expected to announce next week the name of the successor to Dutt, whom the team hold responsible for the demotion.
Stuttgart will play next season in Bundesliga's second division for the first time in 41 years, after losing 1-3 against Wolfsburg in their final match.
Club president Bernd Wahler resigned last weekend after the defeat against Wolfsburg.
Dutt joined Stuttgart in January 2015.