The home team are currently 18th in the table, three points ahead of the relegation zone, while Burnley are top, 11 points clear of second-placed Sheffield United with five games left.
Match preview
Rotherham United will enter Tuesday's contest off the back of a 2-0 home loss to Luton Town on Saturday, with the result leaving them in the relegation mix entering the final straight.
Matt Taylor's side have picked up 45 points from their 41 league matches this season, which has left them 18th in the table, just three points clear of the relegation zone, so they will certainly be looking over their shoulder at a vital stage of the campaign.
The Millers finished second in League One last season to earn promotion back to this level, so finishing 21st or higher would go down as a successful campaign.
Rotherham have only won one of their last six league matches, which is slightly worrying form considering their position in the table, and they will now be taking on the best side in the division.
Taylor's team have picked up 29 points from their 20 home league games this term, but they will be welcoming a Burnley outfit with the best away record in the division, securing 40 points from 20 matches.
Burnley secured promotion back to the Premier League with a 2-1 success over Middlesbrough on April 7, and they are now closing in on the title in England's second tier.
Indeed, Saturday's goalless draw with Reading left them 11 points clear of second-placed Sheffield United with five games left, leaving them in a commanding position when it comes to winning the league.
The Clarets have won 26, drawn 13 and lost two of their 41 league games this term to collect 91 points, and they are unbeaten in England's second tier since the start of November, which is an indication of the size of the task facing Rotherham in Tuesday's contest.
Burnley were relegated from the Premier League last season, but they have been able to bounce back at the first time of asking, and it will be fascinating to see how the team perform next term if Kompany remains as head coach, which is far from certain considering his success at the helm.
The Clarets have won each of their last four matches against Rotherham, including a 3-2 success in the reverse game at Turf Moor back in November, with their last loss against the Millers coming in May 2004.
Rotherham United Championship form:
L
L
D
W
D
L
Burnley Championship form:
W
W
D
W
W
D
Burnley form (all competitions):
W
L
D
W
W
D
Team News
Burnley will be without the services of their leading goalscorer Nathan Tella, with the on-loan Southampton attacker picking up an injury in the early stages of the clash with Reading.
However, Benson Manuel's late withdrawal was due to cramp, and the Belgian is expected to be available for selection on Tuesday night.
Kompany made wholesale changes to his side against Reading on Saturday, but the majority of their key players should return here, with Ashley Barnes, Jack Cork and Arijanet Muric set to be among those to start.
Rotherham, meanwhile, will be missing Conor Washington, Viktor Johansson, Bailey Wright, Grant Hall, Sean Morrison and Ben Wiles for Tuesday's contest.
Head coach Taylor is expected to resist the temptation to shuffle his pack following the defeat to Luton, with a 3-5-2 formation set to include Jordan Hugill in the final third of the field.
However, there could be a change in a wide area, with Domingos Quina potentially coming in for a start, while Oliver Rathbone will also be in the manager's thinking when it comes to potential alterations.
Rotherham United possible starting lineup:
Vickers; Peltier, Humphreys, Blackett; Harding, Lindsay, Coventry, Fosu, Quina; Ogbene, Hugill
Burnley possible starting lineup:
Muric; Roberts, Harwood-Bellis, Beyer, Maatsen; Cullen, Cork, Brownhill; Gudmundsson, Barnes, Foster
We say: Rotherham United 1-2 Burnley
Burnley are closing in on the Championship title, and we are expecting them to win on Tuesday night. Rotherham also need the points in their battle against survival, but we are finding it difficult to back against the Clarets, who should welcome back their key players for this contest.