Kenny has reshaped the squad he inherited from Mick McCarthy and attempted to instil a new brand of football, but is yet to taste victory in his nine matches to date, the most recent of them Saturday's 3-2 World Cup qualifying defeat in Serbia.
Here, the PA news agency takes a look at some of the talking points surrounding the Group A clash in Dublin.
Dara or Duffy?
Central defender Shane Duffy played every minute of Kenny's first eight games, having established himself as a mainstay of the team under predecessors Martin O'Neill and McCarthy and also standing in as captain in Seamus Coleman's absence. However, having lost his place at Celtic after a difficult run of form and therefore short of football when he reported for international duty, he found himself sitting on the bench in Belgrade as Dara O'Shea got the nod alongside Ciaran Clark. A towering presence at the heart of the Irish defence, Duffy still has a role to play, but 22-year-old O'Shea has stepped up impressively and represents genuine competition.
Changing of the guard
It was perhaps significant in Serbia that Robbie Brady and Jeff Hendrick, the stars of Ireland's Euro 2016 finals adventure, and James McClean, whose goals in the last World Cup qualifying campaign proved so important, were used only as substitutes. The midfield trio which started the game at the Rajko Mitic Stadium instead comprised 21-year-old Jayson Molumby, Josh Cullen, 24, and senior partner Alan Browne, himself only 25, and although largely inexperienced at international level, reflected the manager's desire to play a more possession-based game. Their retention might send a message as to his plans for the way forward.
The foot injury Aaron Connolly suffered in Serbia is a blow, but he is yet to open his goalscoring account after six appearances. Of the remaining members of the striking pool, Shane Long has 17 goals to his name, but none since he found the back of the net in Moldova in October 2016, James Collins two – he got the second in Belgrade after coming off the bench – and Callum Robinson one, with Troy Parrott also yet to register. All four will hope for a chance to add to their respective tallies.
Those were the days
Should the Republic fail to emerge with three points, they will assemble for their next round of fixtures in September having gone more than two years and 13 games without a competitive win. Their last victory came in a Euro 2020 qualifier at the Aviva in June 2019 when a Joseph Chipolina own goal and a late Brady strike secured a 2-0 win over minnows Gibraltar.
This will be the first meeting between Ireland and Luxembourg, who are no longer a soft touch in international football. They finished second in their Nations League C group, winning three of their games and drawing a fourth, with their most impressive result a 2-1 away victory over Montenegro, who ultimately topped the table. They fared less well, however, in the Euro 2020 qualifiers, where all four of their points in a group which also included Ukraine, Portugal and Serbia, were claimed against bottom-of-the-table Lithuania, and lost 1-0 to World Cup hosts Qatar in a friendly in Hungary in midweek.