Emirates club hope to negotiate with St Mary’s club.
Southampton have dismissed Arsenal’s £6million bid for winger Alex Oxlade-Chamberlain and are holding out for £12million.
The 17-year-old has been on the Gunners radar for some time but the Saints will only sell for the right price.
The Championship club executive chairman Nicola Cortese is believed to have thrown the offer in the bin and told his Arsenal counterpart to only come back if they are prepared to offer serious money.
Arsenal could face competition from Liverpool and Manchester United, but north London is the player’s preferred destination.
“It was regarded as derisory, and would not have been accepted even if the club had been on the brink of bankruptcy,” an insider told the Daily Star.
Meanwhile, the Gunners are at least hoping to complete the signing of Ivory Coast striker Gervinho in an £11million move before the weekend.
Manager Arsene Wenger is also confident of signing Valencia winger Juan Mata to play alongside midfielder Samir Nasri, and not to replace the Frenchman.
The Spanish 23-year-old does have a €25million release clause but will only come into effect if another La Liga club want to make an offer.