The Hatters required a replay to edge past Wigan Athletic in the previous round, while the Mariners have beaten League One trio Plymouth Argyle, Cambridge United and Burton Albion en route to the fourth round.
Match preview
Luton have played five games since the turn of the year and three of those have been against Wigan, including two fixtures in the FA Cup, with a 1-1 draw on home soil followed by a 2-1 away victory in the replay to help the Hatters progress to the fourth round for the third successive season.
Elijah Adebayo was on the scoresheet in Luton's replay triumph and he also found the net against the Latics four days later as Rob Edwards's side secured a 2-0 Championship win at the DW Stadium on Saturday.
Luton have won five of their last seven games across all competitions and have climbed up seventh in the second-tier standings, sitting just outside the playoffs on goal difference.
The Bedfordshire-based outfit now turn their attention to the FA Cup and will attempt to reach the fifth round in consecutive seasons for the first time since 1984-85 and 1985-86 - the Hatters secured a 3-0 fourth-round win over Cambridge last season before losing 3-2 at home to eventual finalists Chelsea in the fifth round.
Luton's last encounter with Grimsby was when they plied their trade in League Two in the 2017-18 campaign, and they came out on top in both home and away fixtures without reply, with a 2-0 home win in December 2017 followed by a narrow 1-0 away victory in January 2018.
Grimsby, meanwhile, have had two weeks off after seeing their League Two fixture against Crawley Town postposed last weekend due to a frozen pitch.
The Mariners' last outing ended in disappointing fashion as they lost 5-0 with 10 men away at Swindon Town on January 14. Paul Hurst's side were only a goal down heading into the final half hour, but they capitulated in the latter stages of the second half and ultimately suffered their 10th league defeat of the season.
Grimsby, who were promoted from the National League last season, are on course for a mid-table finish in League Two this term as they currently sit in 16th place, 10 points clear of the relegation zone and 11 behind the playoffs.
Hurst is now preparing his side for their first FA Cup fourth-round tie since the 1999-2000 campaign when they lost 2-0 to Bolton Wanderers - the last time that they reached the fifth round was in 1995-96 under the tutelage of Brian Laws when they secured a 3-0 win in a replay against West Ham United.
Grimsby will be regarded as underdogs for Saturday's clash with Luton, but they have won both of their previous two FA Cup meetings with the Hatters, claiming a thrilling 4-3 away victory in January 1950 before cruising to a 7-1 home win in January 1996.
Luton Town FA Cup form:
D
W
Luton Town form (all competitions):
W
W
D
L
W
W
Grimsby Town FA Cup form:
W
W
W
Grimsby Town form (all competitions):
W
L
L
W
W
L
Team News
Luton will be without Luke Freeman, Henri Lansbury, Sonny Bradley and James Shea as they continue to recover from injury, while top scorer Carlton Morris and Cauley Woodrow are both doubtful.
James Bree has played his final game for the club after completing a permanent move to Nathan Jones's Southampton, so either Alfie Doughty or Fred Onyedinma could be handed a start at right wing-back.
Dan Potts, Tom Lockyer and Gabriel Osho are all set to retain their places in the back three, while Allan Campbell could be recalled in centre-midfield at the expense of Louie Watson.
As for Grimsby, Ryan Taylor, Jordan Cropper and Lewis Richardson are set to remain out with injuries, while captain Luke Waterfall returned to light training last week but remains doubtful for Saturday.
Luton loanee John McAtee is ineligible to face his parent club, while Preston North End loanee Mikey O'Neill is cup-tied having already played in the FA Cup with the Championship club this season.
Midfielder Harry Clifton is Grimsby's top scorer so far this season with six goals, and he is expected to retain his place in the middle of the pitch alongside Gavan Holohan and Bryn Morris.
Luton Town possible starting lineup:
Horvath; Osho, Lockyer, Potts; Doughty, Campbell, Clark, Mpanzu, Doughty; Adebayo, Cornick
Grimsby Town possible starting lineup:
Crocombe; Efete, Smith, Maher, Driscoll-Glennon; Green; Morris, Clifton, Holohan; Khan, Kiernan
We say: Luton Town 2-0 Grimsby Town
Luton have won each of their last 16 FA Cup ties as a Football League club against teams from a lower division, and they will be regarded as favourites to come out on top on Saturday.
Grimsby, meanwhile, have struggled away from home in recent weeks, losing five of their last six matches on the road, and another defeat could be on the cards at Kenilworth Road.