Wolves picked up their first league win of the season last time out.
A narrow 1-0 victory over Southampton was a step in the right direction, although fans will be hoping to see more convincing performances in future.
City have played twice in European competition since their last Premier League outing.
A 4-0 win in Seville was followed up with a 2-1 victory over Borussia Dortmund.
Erling Haaland continued his spectacular form with three goals across the two games, taking his tally to 13 from just nine City appearances.
A draw in their last domestic fixture at Villa Park will act as an incentive for Pep Guardiola's side, who will be hoping to leave the West Midlands with all three points this weekend.
The Spaniard is expected to be part of Lage's matchday squad on Saturday, yet it is still unclear whether he is match fit.
Costa joins Wolves after Sasa Kalajdzic suffered an injury to his ACL just 45 minutes into his debut against Southampton.
Raul Jimenez was named on the bench in that match, although was later withdrawn due to a groin issue.
Jimenez will also miss this weekend's clash.
Wolves have no fresh injury concerns. With no natural striker expected to start, Wolves' attack may look different.
Hwang Hee-Chan played up top on the opening day, although Daniel Podence and Goncalo Guedes have both filled in this season.
The Citizens have been plagued with injuries at the start of their title defence.
Centre half Aymeric Laporte is back in first team training, although the trip to the West Midlands comes to soon for the Spanish international.
Sa; Semedo, Collins, Kilman, Jonny; Neves, Moutinho, Nunes; Guedes, Podence, Neto (4-3-3)
Ederson; Cancelo, Dias, Stones, Gomez; Rodri, Gundogan, De Bruyne; Silva, Haaland, Foden (4-3-3)
The Irish international cost Wolves £20 million, a fee which is already looking like a bargain.
Saturday will be Collins' toughest challenge yet, facing City's goal machine Haaland.
With Collins demonstrating that he has the physicality and awareness to succeed at the top level, a good performance on Saturday will be crucial if Wolves are to take anything from the game.
As for Haaland, there is not much left to say that has not already been said.
The Norweigan international scored 10 goals in his first six Premier League games, including back-to-back hat-tricks at The Etihad.
His performances earned him Player of the Month at the first time of asking, the first player to do so since Bruno Fernandes in February 2020.
Haaland has a certain air of inevitability, showcased perfectly on Wednesday night.
City's number nine had struggled to get himself into the game before producing a moment of magic to seal all three points.
It will come as a shock if Haaland leaves Wolverhampton without hitting the back of the net.
Where is the game being played?
The game will be played at Molineux Stadium, Wolverhampton.
What time is kick-off?
Kick-off is at 12:30pm BST.
How can I watch?
For fans in the UK, the game will be live on BT Sport Ultimate, BT Sport 1 and BTSport.com.