The hosts were beaten 2-1 away at Reading in Neil's second game at the helm on Sunday, while their visitors remained just a point better off than their opponents following a defeat to Wigan Athletic by the same scoreline.
Match preview
Stoke City experienced a tough start to the season under the management of Michael O'Neill, and, following a defeat to Sunderland which left them on four points from five outings, he was dismissed with the Potters quickly eyeing up opposition boss Alex Neil.
The Scotsman was then in attendance to watch them beat Blackburn Rovers 1-0 away from home late in August, courtesy of Lewis Baker's goal, before taking the reins the following day, with his first test coming at home to Swansea City.
They trailed for almost the entirety of that game, following Joel Piroe's sixth-minute opener for the visitors, but Stoke were eventually able to snatch a point as Tyrese Campbell netted an equaliser from close range in injury time to force a 1-1 draw.
The Potters then travelled to Reading on Sunday and again trailed from the outset as Lucas Joao capitalised on a goalkeeping error and scored inside the first two minutes, and, while Ben Wilmot did equalise before half time, the Royals would eventually triumph as Joao hit his and his side's second of the game around the hour mark from the penalty spot.
Such a result leaves the Staffordshire outfit 20th in England's second tier with eight points from eight games, and, having overseen a defeat and a draw thus far in his tenure, Neil will be desperate to see them kick on with a victory at the weekend.
Nathan Jones, meanwhile, will make the trip hoping to get one over on his former side as Luton Town also aim to return to winning ways.
In their bid to mount another promotion push this time around, the Hatters were unable to win any of their first four league outings, amassing just two points in the process, before finally putting a victory on the board away at Swansea City as Allan Campbell and Carlton Morris got on the scoresheet.
They then played out a 1-1 draw with league leaders Sheffield United, before making it seven points from the three-match span with a 2-1 win away at Cardiff City, having led 2-0 through Luke Freeman and Gabriel Osho before holding on for the final five minutes as Romaine Sawyers pulled a goal back for the Bluebirds.
Hoping to extend their positive run of form, Jones's side hosted Wigan Athletic last time out and led until the 80th minute thanks to Morris's first-half finish, but a Tom Lockyer own goal drew the visitors level and Thelo Aasgaard popped up with an 88th-minute winner to snatch all three points for the Latics.
On the back of that late disappointment, Luton will look to put a third league win of the season on the board on Saturday and begin a climb up the division.
Stoke City Championship form:
Luton Town Championship form:
Team News
Stoke City continue to deal with several injury issues, as Harry Souttar, Nick Powell, Josh Laurent and Josh Tymon are all sidelined.
Goalkeeper Jack Bonham may see his place at risk with Josef Bursik expected to come in between the sticks, while Neil appears to prefer a back three consisting of Morgan Fox, Aden Flint and Ben Wilmot in the absence of Souttar.
Such a setup could again mean attacker Jacob Brown operates in somewhat of a wing-back role, with Tyrese Campbell and Liam Delap both set to keep their places up front while William Smallbone and Sam Clucas should join Lewis Baker in midfield.
Luton also have injury problems to deal with, as Pelly Ruddock-Mpanzu and Alfie Doughty are out of action alongside goalkeeper James Shea, while attacker Harry Cornick was fit to feature off the bench last time out after a layoff of his own.
He will look to come in from the outset, although there is plenty of competition with Cauley Woodrow, Cameron Jerome and Fred Onyedinma also pushing to replace Elijah Adebayo or Carlton Morris, who has netted three goals in the last four league games following a summer switch from Barnsley.
The front two will be supported by creative midfielder Luke Freeman, who should operate ahead of Allan Campbell and Jordan Clark in the engine room.
Stoke City possible starting lineup:
Bursik; Wilmot, Flint, Fox; Brown, Smallbone, Baker, Clucas, Fosu; Delap, Campbell
Luton Town possible starting lineup:
Horvath; Osho, Lockyer, Potts; Bree, Campbell, Clark, Bell; Freeman; Adebayo, Morris