Both sides were promoted last season, so they will be hoping to deliver their fans with a cup run for them to get behind, too.
Match preview
Indeed, despite only finishing sixth in the National League last season, Grimsby bounced back to the Football League at the first time of asking after a remarkable run through the play-offs.
Paul Hurst's side won after extra-time against each of Notts County, Wrexham and Solihull Moors, with Gavan Holahan's 96th-minute equaliser against the former proving absolutely crucial as The Mariners went on an unforgettable run.
With four points from their opening four matches in League Two, Hurst will be confident his side can avoid becoming embroiled in a relegation battle, while their 4-0 win against Crewe Alexandra in the first round of the EFL Cup was a great way to mark their return to the competition.
Facing a Premier League side such as Nott'm Forest will be a much tougher ask, of course, but the 47-year-old will hope to prey on any major changes in terms of personnel from their forthcoming opponents.
Indeed, Nott'm Forest have adapted to life in the Premier League reasonably well so far, having bounced back from their opening day defeat to Newcastle United by beating West Ham United and claiming a point away to Everton.
Steve Cooper will have been disappointed by his side failing to hold out for a victory at Goodison Park after Brennan Johnson broke the deadlock in the 81st minute, but with so many new signings still bedding in, the former Swansea boss knows he must be patient before expecting any potential fireworks.
Indeed, Forest's lavish spending this summer has caught the eyes of many observers far and wide, with 16 first-team players signed so far for a total of close to £150m.
Tuesday's cup tie at Grimsby could provide the perfect opportunity for Cooper to hand some of his fresh faces an opportunity to impress their new boss, but he will be cautious about the possibility of an upset damaging their season.
Grimsby Town EFL Cup form:
Grimsby Town form (all competitions):
Nottingham Forest form (all competitions):
Team News
Hurst picked a strong team in the previous round's crushing of Crewe, so there seems to be no reason as to why the former Ipswich Town boss would change tact against superior opposition.
Danny Amos could slot in at left-back, though, with Ryan Taylor potentially rested in attack to allow Aribim Pepple another shot at leading the line.
Forest, meanwhile, will travel without Moussa Niakhate after the central defender missed Saturday's trip to Merseyside with a hamstring strain likely to keep him out of action for several weeks.
Morgan Gibbs-White made his debut from the bench against Everton following his big-money move and should start here, while Emmanuel Dennis, Remo Freuler, Cheikhou Kouyate, Giulian Biancone and Wayne Hennessey are all in line for full debuts, too.
Omar Richards remains sidelined with a fractured leg, while Jack Colback is unlikely to be risked after his recent bout of illness.
Grimsby Town possible starting lineup:
Crocombe; Efete, Waterfall, Smith, Amos; Wearne, Green, Morris, Holohan, Driscoll-Glennon; Pepple
Nottingham Forest possible starting lineup:
Hennessey; Kouyate, Cook, McKenna; Biancone, Freuler, Yates, Toffolo; Gibbs-White, Dennis; Surridge
We say: Grimsby Town 0-3 Nottingham Forest
With so many new signings likely to be provided with a chance by Cooper at Grimsby, there is a chance the visitors could be a little disjointed.
However, some of the players expected to start have the potential to hugely improve Forest, who could enjoy themselves in Lincolnshire on Tuesday.