The Chilean winger, who would have been out of contract this summer and free to leave the Emirates for nothing, moved to Manchester United in a straight swap for Henrikh Mkhitaryan.
However, according to the Daily Star, Wenger had actually wanted Anthony Martial but both chief executive Ivan Gazidis and new head of recruitment Sven Mislintat disagreed.
It had been assumed that United blocked Arsenals move for Martial, but Wengers interest got no further than a meeting with the rest of the clubs transfer team.
Instead, Mislintat pushed for Mkhitaryan, who he had previously signed for Borussia Dortmund from Shakhtar Donetsk back in 2013.
Wenger, concerned by Arsenals porous defence, had also pushed to try and sign Chris Smalling in January as part of the deal for Sanchez, but the recruitment team did not back his move.
It has also been claimed that Gazidis, not Wenger, was responsible for signing Shkodran Mustafi in spite of numerous scouting reports that doubted his ability.
Although he may not have been Wengers first choice, Mkhitaryan has enjoyed a relatively bright start to his career at Arsenal.
He has four assists in the Premier League since the turn of the year, though three came in one match against Everton, while he also scored at the San Siro as Arsenal cruised past AC Milan in the Europa League.
Wenger announced on Friday that he would step down from his role in charge of Arsenal at the end of the season after a reign that saw him win three Premier League titles and seven FA Cups.
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