The Championship outfit have beaten Ipswich Town and Cardiff City in the competition, and City overcame Newcastle United in the second round last month.
The Hatters currently sit 21st in England’s second tier, while City occupy third position in the Premier League table following Saturday’s win against Tottenham Hotspur.
With attentions now turning to the Carabao Cup, LCFC.com profiles Luton Town…
The manager
Graeme Jones was appointed Luton Town manager in May 2019, having previously spent time as an assistant manager at the Belgium national team and West Bromwich Albion.
Jones worked alongside Roberto Martínez at Swansea City, Wigan Athletic and Everton before joining the Spaniard at the Red Devils.
During his 10 games in charge of the Hatters, Jones has won four fixtures, with two of those triumphs coming in the Carabao Cup.
The squad
This term, Luton have been boosted by the additions of loanees Isaiah Brown (Chelsea), Luke Bolton (Manchester City) and James Bree (Aston Villa).
Meanwhile, Callum McManaman, Brandon Galloway and Ryan Tunnicliffe all have Premier League experience to their name.
En route to the League 1 title, James Collins finished as the division's top scorer with 25 goals, and joined James Justin in the PFA League 1 Team of the Year.
Club captain Alan Sheehan, meanwhile, spent five years at Leicester City, and scored a memorable free-kick in 3-2 win against Nottingham Forest in 2007.
The trophy cabinet
Luton Town famously beat Arsenal 3-2 in front of over 95,000 fans at Wembley Stadium to lift the League Cup in 1988, thanks to a last-minute winner from Brian Stein.
They have won England’s third tier three times, including last season’s triumph, while they have one second division and one fourth division title to their name.
In addition, they won the EFL Trophy in 2009 following a 3-2 victory in extra-time over Scunthorpe United at Wembley.
The stadium
Attracting a sell-out crowd during Saturday’s encounter with Hull City, Kenilworth Road has a capacity of just over 10,000.
The Bedfordshire-based stadium was opened in 1905 and has a record attendance of 30,069 during an FA Cup tie with Blackpool in 1959.
The fixtures
Luton began life back in the Championship with a 3-3 draw with Middlesbrough at Kenilworth Road, as James Collins scored a late equaliser to seal a point.
Defeats to Cardiff City, West Bromwich Albion and Sheffield Wednesday and triumphs over Ipswich and Cardiff in the Carabao Cup and Barnsley and Huddersfield Town in the Championship followed.
However, back-to-back losses to Queens Park Rangers and Hull means Luton will be aiming to return to winning ways on Tuesday.
After the clash with City, Graeme Jones’ side head to Ewood Park to take on Blackburn Rovers in the Championship.