The Foxes, who defeated the Seagulls in the Premier League back in December, have reached this stage after victories over Stoke City and Brentford, while Graham Potter's men overcame Newport County and Blackpool in earlier rounds.
Ahead of Wednesday's Filbert Way fixture, LCFC.com takes a detailed look at Graham Potter's men...
The manager
Former Stoke City, West Bromwich Albion and York City left-back Graham Potter signed a four-year contract as Brighton's manager in the summer of 2019, following one year at Swansea City.
The Seagulls made an assured start to the 2019/20 season following his appointment, securing wins over Watford, Tottenham Hotspur, Everton and Norwich City.
However, Leicester’s 2-0 victory at AMEX Stadium in November put a halt to their good run of form and the South Coast outfit would only record two more league wins before the postponement of Premier League football in March.
At the end of the 2019/20 season, Brighton finished in 15th place, seven points clear of danger.
After graduating from the Open University with a degree in Social Science, working for the University of Hull as a football development manager and as a technical director for the Ghana women's team, Potter also completed a master's in Leadership and Emotional Intelligence, before going into professional football management.
Potter's career began at Östersund in Sweden, where he led them from the fourth tier to the Allsvenskan, the country's top division, eventually also winning the Svenska Cupen, or Swedish Cup.
That latter success qualified his side for the second qualifying round of the 2017/18 UEFA Europa League, where they would defeat Turkish giants Galatasaray 3-1 over two legs.
Also overcoming Fola Esch and PAOK, Östersund eventually reached the group stage and would finish second, level on points with Athletic Bilbao, seeing them into the knockout round.
Potter and his resilient, skilful side truly made headlines in England by sealing a remarkable 2-1 victory over Arsenal at Emirates Stadium, but would eventually suffer an aggregate defeat in 2018.
In the following summer, Potter moved to Swansea City, reaching the quarter-finals of the Emirates FA Cup, finishing 10th in the Sky Bet Championship and building a youthful, talented squad.
The team
Brighton's squad was bolstered with several exciting summer signings, including Adam Lallana, on a free transfer from Liverpool, and Danny Welbeck, who also joined on a free from Watford.
Right-back Joël Veltman signed from Ajax, while centre-back Ben White decided to remain at AMEX Stadium, despite reported interest from Leeds United, after an impressive loan spell at Elland Road.
Ben White, Adam Webster, Pascal Groß and Neal Maupay have all featured for the Seagulls on 24 occasions throughout 2020/21 so far.
Former Chelsea youngster Tariq Lamptey, on the other hand, has also earned plaudits for his standout performances at right-back for Graham Potter's men throughout the early months of the season.
Brighton's goalscoring charts are topped by Maupay, with seven strikes in all competitions, while Alexis Mac Allister, Solly March and Lewis Dunk have all netted three goals.
Form guide
The Seagulls go into Wednesday's visit to Leicester unbeaten in their last six games in all competitions - a run of form which has included admirable results.
Neal Maupay's 17th-minute effort on 16 January was enough to secure a 1-0 victory over Leeds United at Elland Road, before a 2-1 Emirates FA Cup success over Blackpool at AMEX Stadium.
A 0-0 home stalemate with Fulham on 27 January was followed, four days later, by a 1-0 triumph over Tottenham Hotspur at AMEX Stadium, with Leandro Trossard finding the net early on, before a stunning result at Anfield.
After frustrating the reigning champions in the first period, Steven Alzate struck for the Seagulls to give Brighton a 56th-minute lead on Merseyside - which they would defend valiantly in another 1-0 victory.
More recently, on Saturday, Brighton had to settle for a point at Turf Moor as Burnley midfielder Jóhann Berg Guðmundsson equalised Lewis Dunk's opener.
Previous encounters
Leicester City are unbeaten in their last seven clashes with Brighton, all spanning over their shared time in the Premier League, while the Seagulls last enjoyed success in April 2014.
Last term, the Foxes secured a 2-0 victory at AMEX Stadium, courtesy of goals from Ayoze Pérez and Jamie Vardy, while the two sides played out a goalless stalemate at King Power Stadium.
Earlier this season, at King Power Stadium, James Maddison netted a brace and Vardy registered on the scoresheet once as a stunning first-half performance helped City secure a 3-0 victory over Brighton on 13 December.
In total, City have won 16 times against Brighton, who themselves have tasted victory on 13 occasions, while seven matches have ended in draws.
The trophy cabinet
Three-time third tier champions Brighton (1958, 2002 and 2011) have also finished as runners-up in the second tier twice, in 1979 and, most recently, in 2017.
Over their history, the Seagulls have also won the fourth division twice, in 1965 and 2001, while lifting the Southern Football League title back in 1910.
In domestic cup competitions, meanwhile, the South Coast side were FA Cup runners-up in 1983, losing a replay to Manchester United, and FA Charity Shield winners in 1910.
The stadium
AMEX Stadium, Brighton's home since 2011, is among the most picturesque venues in English football, surrounded by woodland and including an iconic curved design to its four stands.
Based in the village of Falmer, the 30,750-capacity ground was built after Brighton left the Goldstone Ground in 1995 with no permanent new home arranged.
After ground sharing at Gillingham's Priestfield Stadium for two seasons, 50 miles away in Kent, the club then moved to Withdean Stadium, where they remained between 1999 and 2011.
After expansion work since its opening in 2011, AMEX Stadium allows Brighton to regularly attract crowds in the region of 30,000, while also providing a day-to-day home for the club.
Upcoming fixtures
Brighton welcome Aston Villa to AMEX Stadium on Saturday (8pm kick-off) before also entertaining rivals Crystal Palace on 22 February (8pm kick-off).
The Seagulls head to The Hawthorns on 27 February to tackle West Bromwich Albion (3pm kick-off), before Leicester are visitors to Brighton on 6 March (3pm kick-off).
All times GMT.