Nigel Pearson's men may have accrued just one Premier League point since winning the Championship last term, but their performances have offered cause for optimism.
Having twice fought back to draw 2-2 against Everton on the opening day, Pearson's charges held out for over an hour against title favourites Chelsea before succumbing to a 2-0 defeat.
Tuesday's League Cup loss at home to League Two Shrewsbury Town will have been a concern, though, and Leicester must now overcome last season's FA Cup winners if they are to avoid ending August without a win.
Arsenal, on the other hand, are looking to complete the month unbeaten, having won the Community Shield, qualified for the UEFA Champions League group stage and taken four points from two league games.
With a return to the Champions League for a 17th consecutive season also secured courtesy of a 1-0 aggregate win over Besiktas, Wenger is now braced for another tough test this weekend against a side buoyed by the signing of experienced midfielder Esteban Cambiasso.
"They have been impressive in their first two games. They had a very good result against Everton... and at Chelsea they played very well," the Frenchman said on Friday.
"They are a team who have very good defensive solidity, they are very good at counter-attacking and they have good players on the flanks who are very quick.
"They have bought Cambiasso from Inter Milan, a very good, intelligent player - it will be a big, big challenge for us."
Late goals have been a theme for Wenger's side. Aaron Ramsey's last-minute winner against Crystal Palace was followed up by two dramatic goals to secure a draw at Everton last Saturday.
The 2-2 Goodison Park scoreline was earned courtesy of strikes from Ramsey and Olivier Giroud in the final seven minutes, but came at a cost, with the France striker picking up an ankle injury that will sideline him long-term.
Despite the absences of Giroud and Mikel Arteta (ankle), Pearson believes his opposite number still has plenty of quality at his disposal.
"We know it will be another tough game for us but I expect our players to cause them problems and we have spoken about the best ways that we operate to try and get the three points," he told Sky Sports.
"That's what we will be about every time that we play. Whether we can achieve it against sides like Arsenal remains to be seen, but I would think that having seen our first two games they will know it is a difficult tie for them."
Wenger can welcome Ramsey back following his suspension in Europe on Wednesday, although goalkeeper David Ospina (hamstring) remains a doubt having only returned to full training recently, with Kieran Gibbs (hamstring) also absent.
Danny Drinkwater (hamstring) and Jamie Vardy (thigh) could make their Leicester returns, while Matty James (shin) and Matthew Upson (foot) look set to miss out.
