Gers boss Walter Smith hopes Weir, 39, will recover from an ankle knock in time to play against Markus Babbel's men at the Mercedes-Benz Arena.
"We have a doubt over him," Smith told BBC Scotland.
"Your central defensive partnership is a big thing, especially when you go away from home to play.
"David was a big part of our last Champions League campaign, along with Carlos Cuellar (now with Aston Villa)."
Stuttgart have had a disappointing start to the German Bundesliga season and currently find themselves in 12th place after winning just one of their first five league games, having finished third in the 2008/9 campaign.
Looking ahead to Wednesday's match, striker Kenny Miller added: "If we are being honest, we are not playing up to our full potential either this season so it is a big game for both teams.
"We want to use this as a kick-start and hopefully get some form going in the league as well.
"Obviously it is a big game for them, but also it is a huge game for us as well."
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Source: Team_Talk