The Southampton boss is reportedly ahead of Diego Simeone and Laurent Blanc in the Gunners' thinking.
The Gunners boss has come under increasing pressure this season as he has watched his side’s title hopes fade away.
They are now scrambling to secure a top four finish and that has led to increased calls from the fans for the long serving manager to end his reign at the Emirates.
That is unlikely to happen at the end of this season, with an exit in the summer of 2017 when his contract expires looking the more likely option.
The club has no desire to sack Wenger and will instead allow him to leave on his own terms, and when that happens Koeman would be top of the shortlist to replace him according to the Sun.
Atletico Madrid manager Diego Simeone is also on the list, as well as Paris St Germain’s Laurent Blanc, but neither is as appealing as the Dutchman.
The Arsenal hierarchy have been impressed by Koeman's work since replacing Mauricio Pochettino two years ago, while his football philosophy fits with what Arsenal want from their manager.