Meanwhile, the away side set out to return to winning ways off the back of seeing their perfect start to the campaign come to an end last time out.
Match preview
Luton came away empty-handed from the second game running as they fell to a 3-0 defeat against Chelsea in Friday's encounter at Stamford Bridge.
Goals in either half from Raheem Sterling left Rob Edwards's men with a near-unassailable task before Nicolas Jackson put the result beyond doubt 15 minutes from time.
One of four teams still yet to pick up a point so far, the Hatters sit bottom but one in the Premier League table, albeit with a game in hand.
Awaiting them next is the challenge of an opposing outfit who boast just one victory from the most recent six meetings involving the sides.
Currently on a run of six and two draws from their last eight matches on home turf, Tuesday's hosts will be keen to secure a much-needed win in front of their fans to help kickstart their season.
Gillingham claimed a shock 3-1 win over Southampton in the first round of the EFL when the teams went head to head at Priestfield Stadium on August 8.
Ashley Nadesan's opener and a second-half double from Robbie McKenzie put Neil Harris's men in the driving seat after which Carlos Alcaraz pulled one back.
That was the second of five consecutive victories for the Gills who, however, suffered a 3-0 thrashing at the hands of Colchester on Saturday.
Having won seven consecutive away matches without conceding, Tuesday's visitors will be full of confidence ahead of what is set to a tough assignment against more illustrious opponents.
Luton Town form (all competitions):
D
W
D
L
L
L
Gillingham EFL Cup form:
W
Gillingham form (all competitions):
W
W
W
W
W
L
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Team News
Luton Town English duo Jordan Clark and Dan Potts are currently battling with ankle injuries and will not be playing any part in this one.
Twenty-five-year-old Gabriel Osho also misses out for the hosts through a knee problem he sustained in the promotion playoff final in May.
Ross Barkley could be set to retain his place in the starting lineup after making his debut for his new employers against Chelsea last time out.
Gillingham's Ethan Coleman is ineligible to feature here as he serves a suspension having been given a straight red card in his side's defeat to Colchester.
This could see Jayden Clarke come into the XI for what would be only a second start of the season and a first in five matches across all competitions.
Luton Town possible starting lineup:
Kaminski; Giles, Bell, Lockyer, Burke, Kabore; Barkley, Nakamba, Chong; Morris, Adebayo
Gillingham possible starting lineup:
Turner; Alexander, Ehmer, Ogie, Mahoney; Dieng, Clarke; Nichols, Williams, Malone; Nadesan