The Frenchman was speaking ahead of the Gunners' Premier League season opener against the Foxes on Friday night (11 August). Arsenal have thus far signed Sead Kolasinac on a free transfer and Alexandre Lacazette for a club-record fee from Lyon and Wenger has indicated that they are still open to bring in more players before the end of the summer transfer window.
Mahrez was on Arsenal's radar last summer fresh from his exploits to help Leicester win the league title, but he chose to remain at the King Power Stadium for another season agreeing to a new deal until the summer of 2020. The Algerian failed to replicate his form during the last campaign and this summer made it clear that he wants to leave in search of a new challenge.
Arsenal were linked with a move for him earlier in the window, but speculation has subsided with AS Roma and Inter Milan now in the driving seat to take him to the Serie A. Leicester value him at around £50m ($69.4m) and no clubs have managed to meet their valuation thus far.
Wenger has now distanced Arsenal from a potential move stating that the club already has a number of players similar to the Algeria international. The French coach is keen to strengthen the squad and confirmed that they are open to further additions, but it is likely to happen only after they trim the senior squad, which already consists of 33 players.
A number of players have been deemed surplus to requirements, but the club is finding it hard to offload them either due to the player's wage demands or interested clubs failing to meet Arsenal's valuation of a certain player.
"We were never close. I rate him [Mahrez] as a player but we have similar types with Alex Iwobi, Jack Wilshere back, Mesut Ozil - we have plenty of the same type of players," Wenger said, as quoted by Goal.
"We are still open. But of course at the moment I have currently 33 players and it is very difficult to manage on a daily basis such a high number," the Frenchman added.
Meanwhile, Wenger believes Manchester City have had the best summer thus far owing to Pep Guardiola's £200m+ outlay to sign six players. Manchester United and Chelsea are also not too far behind with both clubs having spent close to £150m thus far.
The Arsenal boss expects all teams to strengthen further before the window shuts on 31 August, and believes it is one of the reasons that makes the upcoming campaign unpredictable.
"Yes, because look at what City have done. They have been quite spectacular in the transfer market, Manchester United as well," Wenger said.
"And it's not finished – Chelsea have bought [Alvaro] Morata and have not lost [Diego] Costa yet, and they will certainly buy more. In the middle of the transfer market it's difficult to predict [the season].
"At the moment the most active have been United, City and Liverpool a bit," the French coach explained.