The La Liga high-flyers top Group G after winning their opening three matches and will enter the home fixture against their struggling opponents as red-hot favourites.
Atletico have won 11 of their 12 league fixtures this season, helping them to second place in the table, just one point behind Barcelona.
Costa has been outstanding for Diego Simeone's side, scoring 15 goals in as many appearances in all competitions.
His latest effort - which came in Sunday's 2-0 home success against Athletic Bilbao, when Villa also scored to take his tally to seven - led Simeone to lavish him with praise.
"Diego is huge in every way," Simeone said. "On top of the goal he scored, he is growing as a player – he is more of a team player and helps us win the ball back.
"All of that makes the whole team play better. We hope he continues to grow because he's got many years ahead of him to get even better."
Costa missed the first two matches of this year's group stage due to a suspension incurred in last season's Europa League, but he scored twice in Atletico's 3-0 win at Austria Vienna last month.
Austria Vienna sit on the bottom of Group G with just one point from their three matches and the visitors' league form suggests an upset is highly unlikely.
Head coach Nenad Bjelica – who will serve a touchline ban for the fixture – saw his side win just one of 12 matches before Sunday's triumph.
Their goalless draw against Zenit last month was the first Champions League point won by an Austrian side since 2001 and their inexperience is highlighted by the fact that just two of their players – strikers Tomas Jun and Roman Kienast – have played in Europe's premier club competition before this season.
