The Brazil-born Spain international, who helped to knock out Chelsea in the semi-finals on his way to last year's final with Atletico Madrid, has set the Premier League alight following his move to Stamford Bridge in July.
After four goals in his first three matches, Costa netted a hat-trick as Chelsea came from behind to beat Swansea City 4-2 on Saturday.
That impressive haul sees the 25-year-old already four goals clear of his closest challengers at the top of the English top-flight scoring charts, and Chelsea will want to see that form transfer to European competition.
Costa's start to life at in west London has prompted some to draw comparisons with legendary Chelsea strikers such as Didier Drogba, but the imperious forward is keen to carve out his own distinct reputation.
"It is different for every striker who comes here," he said. "Every striker has their way of playing and their strengths and a different team behind them. That is very important.
"If you do not have the team behind you then you can't do things on your own. It all depends on the team. It could be because of that.
"I try to play in the best manner, and hopefully things will continue like this. But there will be a moment when I cannot score - that is football."
Manager Jose Mourinho, whose side top the Premier League with maximum points from four fixtures, described Costa as a "risk and a doubt" for Wednesday's Group G opener, but conceded that had been the case for most of the season so far.
In contrast to Mourinho, Schalke coach Jens Keller finds himself under increasing pressure after failing to secure a win from their opening three Bundesliga matches.
Despite registering a draw against champions Bayern Munich in their second fixture, Schalke have lost at Hannover and Borussia Monchengladbach.
Injury-hit Schalke, who also crashed out of the DFB-Pokal at the hands of Dynamo Dresden, were 4-1 losers at Gladbach on Saturday in a performance Germany international Benedikt Howedes described as "catastrophic".
Keller was without the likes of Felipe Santana (adductors), Joel Matip (adductors) and Jan Kirchhoff (knee) in that defeat, while Julian Draxler and Max Meyer started on the bench.
Fabian Giefer (adductors), Sead Kolasinac (knee), Leon Goretzka (hamstring) and Jefferson Farfan (knee) are all long-term absentees.
Asked whether his side could welcome any players back to the starting XI for Wednesday, Keller claimed: "The question isn't who will be back in time for the next game, but rather will anyone else be ruled out for it."
Chelsea are monitoring the fitness of striker Didier Drogba after he missed the clash with Swansea due to an ankle injury.
These sides meet in the group stage for the second season in succession, with Chelsea having won both meetings 3-0 in the 2013/14 campaign.
Schalke may take some encouragement from the fact that the scorers of five of those goals - Fernando Torres (two), Samuel Eto'o (two) and Demba Ba - have since left Stamford Bridge.
