Villa boss Martin O'Neill must pull out all the stops if he is to land Jovanovic ahead of the Bundesliga outfit.
A close friend of Jovanovic told the Daily Star Sunday: "Aston Villa have made it clear they would love to sign Milan - and the deal is possible. Milan has already turned down the chance to play for Real Madrid, Everton and Spurs.
"Now, it is a straight choice between Villa and Stuttgart.
"At the moment, though, the Germans are favourites - and maybe Villa have only a few days to change that."