The Austrian international played a key role for his side last season, scoring 6 goals in 15 Bundesliga games to help Stuttgart avoid relegation from the Bundesliga.
Despite preserving his club's place in the top flight, Kalajdzic has been linked with a move away from the Mercedes-Benz Arena, with his contract set to expire next summer.
According to Sky Sports News, Manchester United are interested in signing the striker as they look to strengthen in the final third.
The report states that the Red Devils have already held talks to discuss a potential transfer, although no offer has been made for the 25-year-old.
If United decided to move for the striker then they could face competition from other Premier League Clubs, with West Ham United, Brighton & Hove Albion and Southampton all credited with showing an interest.
Kalajdzic, who has scored 24 goals in 57 appearances for Stuttgart, is reportedly keen on a move to the Premier League.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen