Wenger is desperate to strengthen his depleted squad following their nightmare start to the new season, after watching his side suffer at the hands of Aston Villa, who took all three points at the Emirates stadium on Saturday having claimed a well-earned 3-1 win.
And such a disappointing display has prompted the Arsenal chief into taking action, and Richards is one of many players on Wenger's transfer hit-list with around two weeks of the window remaining.
The 25-year-old full-back is not thought to be part of Manuel Pellegrini's plans at Manchester City, and was omitted from the match day squad altogether for their 4-0 win against Newcastle United on Monday evening.
However, an injury to captain Vincent Kompany could cast doubt over a move to Arsenal before it has even begun, though the England international may be keen to make the move to Emirates, particularly with the World Cup just around the corner.
With Richards seemingly out of the first-team picture at the Etihad, a switch to Arsenal may appeal to the Citizens' defender - particularly as he is an Arsenal fan - and his potential signing would solve the Gunners' injury crisis in the process.
Should Ricahrds sign for Arsenal, the move would free up Bacary Sagna to move across to centre-half as cover for the suspended Laurent Koscielny - who was sent off in the north London outfits' horrific opening day encounter.
No price has been quoted as of yet, but Wenger is expected to test the waters with an opening bid this week as he looks to splash the cash to appease the increasingly restless Arsenal fans.
Whether moving for a player deemed not good enough for the Manchester City first-team will help silence the doubters remains to be seen, but it is at least an acknowledgement that Arsenal must improve ahead of the window closing on September 2.