The Gunners are lining up the France international with a deal for Real Madrid midfielder Sami Khedira looking unlikely due to his wage demands.
Arsene Wenger has identified the France international to fill the holding-midfield role at Emirates Stadium next season.
The Gunners have been in contact with Real Madrid about a move for Germany World Cup winner Sami Khedira but a deal is considered unlikely unless the midfielder reduces his demand for a 250,000 euro-a-week basic salary.
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There is also interest from Arsenal in Bayer Leverkusen's Lars Bender but the club regards Schneiderlin as a more realistic target. The Gunners rate the 24-year-old in the €19 million bracket, while Southampton values him at around €22.5 million.
The Saints want to play hardball over any deal following the departures of Luke Shaw, Adam Lallana and Rickie Lambert this summer, as well as former manager Mauricio Pochettino.
It is an exodus that has encouraged others to consider their options and Schneiderlin went public last month with his eagerness to try a new challenge.
"I've been there for a long time now," said Schneiderlin when asked about his future. "We'll see how things go, but the directors know my position and what my intentions are.
"Everyone has ambitions, everyone has his own future in his hands, so we’ll see. Every player wants to play on big occasions."
Schneiderlin has been closely trailed by the Gunners over the last two seasons since Southampton was promoted to the Premier League.
He has been a key performer for the Saints following a move from Strasbourg in 2008 and was drafted into the France squad for the World Cup as a late replacement for the injured Clement Grenier.
Arsenal was weighing up a double swoop for Schneiderlin and his teammate Dejan Lovren, as the Croatian has asked Southampton for a transfer to a club which can offer Champions League football. Liverpool now leads the race to sign the center back.