Sportsmail understands that the Gunners have been closely monitoring the central midfielder in recent weeks with a view to a summer swoop.
Arsenal will assess Schneiderlin on Sunday against Manchester United at St Mary’s Stadium before drawing up a final scouting report on the Frenchman.
The Londoners rate Schneiderlin highly and have placed him on their target list as they prepare to buy a dynamic midfield anchorman this summer.
Mikel Arteta turned 32 in March and has only a year remaining on his contact, while Mathieu Flamini is regarded as a back-up option rather than a first-team regular.
Arsene Wenger is willing to spend up to £15m on Schneiderlin, who has been a virtual ever-present in the Southampton team since joining the club from Strasbourg in 2008 and has been a key figure in their rapid rise from League One to established Premier League outfit.
The Frenchman has grown in stature under Mauricio Pochettino, whose own future is shrouded in doubt as Tottenham prepare to make an approach to Southampton to interview him for what is expected to be their vacant managerial slot at the end of the season.
The Saints are bracing themselves for offers for a number of their key players this summer following a fine campaign in which they are guaranteed an eighth-place finish following United’s win over Hull City last night.
In addition to Schneiderlin, Luke Shaw, Adam Lallana and Dejan Lovren are also targets for the Premier League big spenders.