The visitors, meanwhile, are also searching for their first win of the season after taking only point from their first two matches.
Match preview
After reaching the playoffs last season, Luton will be dreaming of another push for the Championship top six this time around.
They began the campaign with a goalless home draw against Birmingham City before travelling to Turf Moor on Saturday for their first away encounter of the season.
Dan Potts got the Hatters off to a perfect start, grabbing the opening goal in the fifth minute, however, a second half equaliser from Josh Brownhill ensured Luton had to settle for a point.
Following consecutive draws, Luton will now turn their attention to Tuesday's cup game, with the hosts looking to avoid a first-round exit for the second straight season.
Luton can take inspiration from the fact that before last term they progressed from the first round in the previous two campaigns.
Newport County, meanwhile, will be looking to improve upon last season's 11th place finish this time around, as they attempt to make a League Two playoff push.
Like Tuesday's hosts, the Exiles are also yet to win this season, with their opening two league games yielding a single point.
They fell behind in the 24th minute in their season opener against Sutton United, but Omar Bogle equalised before half time to clinch a point for his side.
However, there was to be no equaliser on Saturday when Newport played host to a Walsall side managed by former Exiles boss Michael Flynn, with a Mickey Demetriou own goal condemning the hosts to a 1-0 defeat.
After failing to win any of their opening two games, Newport will now attempt to pull off an EFL Cup upset against a Championship side as they look to progress from the first-round for the second straight season.
Luton Town form (all competitions):
Newport County form (all competitions):
Team News
Luton Town are unable to call upon the services of Louie Watson and Fred Onyedinma, who are both sidelined with injury issues.
Jones may opt to rest a number of players for Tuesday's EFL Cup tie, which could result in Tom Lockyer and Reece Burke being given starting places.
Cauley Woodrow is also in contention to feature in the front two, while Carlton Morris may also come into the forward line.
As for the visitors, they could continue with a back three featuring Declan Drysdale, Matt Dolan and Demetriou.
However, James Rowberry may make a couple changes, with Joe Day set to replace Nick Townsend in goal, while James Waite could start in midfield.
Although he failed to find the net on Saturday, Bogle may retain his place in the frontline after scoring in the opening league game.
Luton Town possible starting lineup:
Macey; Lockyer, Bradley, Burke; Bree, Lansbury, Berry, Clark, Bell; Morris, Woodrow
Newport County possible starting lineup:
Day; Drysdale, Dolan, Demetriou; Norman, Bennett, Waite, Wildig, Evans; Bogle, Zanzala