The Blues were beaten 6-0 at the Etihad Stadium on Sunday, but they have performed well in UEFA's secondary competition and are strong favourites to advance through to the next knockout round.
Malmo will be looking to add to Chelsea's woes on Thursday, knowing that a shock victory over the two legs will help them to create some history as they bid to become the first Swedish club to make it to the last-16 stage of this competition.
The Sky Blues surprised many by finishing as runners-up to Genk in Group I, mainly thanks to a couple of wins over third-placed Besiktas, who finished two points worse off.
It was all to play for heading into the meeting between Malmo and Besiktas on the final matchday in December, and it was Uwe Rosler's charges who prevailed 1-0 in Istanbul to leapfrog their opponents into second place.
With their European adventure still alive, Malmo's focus has been solely on pulling off a major upset by knocking out the 2013 winners. If that is to happen, the Swedish side will likely have to take some sort of lead to West London for the reverse fixture a week later.
Malmo are unbeaten in their last eight home games in European competition, including qualifiers, although six of those matches have ended all square. Should the Sky Blues avoid defeat against Chelsea on Thursday, they will be just one game short of their record of 10 set between September 1975 and November 1979.
All seven of their goals in this season's competition have come in the second half of matches, seeing them overcome Besiktas home and away, as well as earning draws against Sarpsborg 08 (also home and away) and Genk.
Crowned Swedish champions for a record 20th time in 2017, Malmo missed out on the chance to qualify for the Champions League this term as they fell short in the third qualifying round, losing to Hungarian outfit Videoton - a side Chelsea know well from the group phase.
Malmo have already fared better than their only previous involvement in this competition, when collecting just a single group-stage point in 2011-12, and now they have post-Christmas football to look forward to on the continent for the first time in 32 years.
Rosler's side have not played a competitive match since their win at Besiktas on December 12 - whether that will be a help or a hindrance will soon become clear.
Recent form in Europa League: LWDDDW
Recent form (all competitions): WDWWDW
Speaking in the wake of his side's six-goal loss at the Etihad Stadium, Maurizio Sarri confessed that he is unsure what the future holds for him at Chelsea. For now, the former Napoli boss remains in place and he has four games in three competitions to prepare for in the space of 10 days.
Perhaps Chelsea's advancement to the final of the EFL Cup, where they will reunite with the Citizens at Wembley Stadium on February 24, is keeping Sarri in a job on the back of crushing back-to-back away defeats at Bournemouth and Man City.
As well as having a cup final to look forward to - if that is the right term - the Blues also face Manchester United in the quarter-finals of the FA Cup next Monday, before welcoming Malmo to Stamford Bridge for the second leg of their first Europa League knockout match four days later.
Sarri will no doubt want this tie as good as wrapped up before the second leg, then, with it coming between two massive fixtures that could determine whether or not he gets a second season at Chelsea.
If three Premier League away defeats in a row is bad for the Blues, going down 2-0 to Arsenal, 4-0 to Bournemouth and 6-0 to Man City, then two cup exits in the space of a week may well bring an early end to his tenure. That may seem harsh, but this is Chelsea we are talking about.
The Europa League has provided Sarri with some joy this season, though, having seen his side cruise through Group L with 16 points from a possible 18.
Chelsea are one of seven teams to remain unbeaten thanks to home-and-away wins over POAK and BATE, but they could not complete the clean sweep as they were held to a 2-2 draw by Vidi in their final group outing.
That draw in Hungary also ended Chelsea's run of eight successive wins in this competition, including their run to the 2013 final when beating Benfica 2-1 to lift silverware under Rafael Benitez.
Still, the Premier League giants are nine games unbeaten in the Europa League and are many bookies' favourites - ahead of Arsenal, Napoli, Inter Milan and Sevilla - to go all the way this time around. The question is, will Sarri still be at the helm for the May 29 final in Azerbaijan should Chelsea get there?
Recent form in Europa League: WWWWWD
Recent form (all competitions): LWWLWL
With the games against Man United and Man City in mind, Sarri will likely stick with his rotation policy in Europa by recalling a number of fringe players.
That could see a rare start for Callum Hudson-Odoi, though the youngster missed a couple of training sessions with illness last week and was not included in the squad to face Man City.
Elsewhere, Olivier Giroud is favourite to get the nod through the middle as he looks to build on his tally of four goals in three Europa League outings - more than in his previous eight appearances combined.
Marcus Antonsson, who has scored five goals in his last six competitive outings - including the winner against Besiktas - should lead the line for Malmo.
Malmo possible starting lineup:
Dahlin; Nielsen, Bengtsson, Safari; Vindheim, Christiansen, Bachirou, Lewicki, Rieks; Rosenborg, Antonsson
Chelsea possible starting lineup:
Caballero; Zappacosta, Cahill, Christensen, Emerson; Kovacic, Ampadu, Loftus-Cheek; Hudson-Odoi, Giroud, Willian
Head To Head
This will be the first competitive encounter between Malmo and Chelsea, though both sides have experience of facing teams from their opponent's country.
Malmo have lost four of their five matches against English opposition in all competitions, the exception being a 2-1 home win against Nottingham Forest in the first round of the 1995-96 UEFA Cup.
Chelsea, meanwhile, have lost none of their previous four encounters against Swedish sides, though their only two previous-such away games ended goalless.
We say: Malmo 0-2 Chelsea
A response is needed from Chelsea on Thursday if they are to get their campaign back on track. Despite a weakened side likely being fielded, the Blues should become the first away team since Paris Saint-Germain in 2015 to beat Malmo at the Swedbank Stadion in a European match.