However boss Ronald Koeman is still looking to bring more players to the south coast club after a summer full of departures.
But according to the Daily Star Southampton have had a bid for Andros Townsend turned down.
Saints reportedly bid £10 million for the winger but it was refused outright by the North London outfit.
It is a case of roles reversed for both clubs after Tottenham Hotspur spent most of the summer trying to lure midfielder Morgan Schneiderlin for St Mary’s.
Both clubs seem unlikely to change their stance on either move and Ronald Koeman may now move for Lazio midfielder Alvaro Gonzalez instead.
The Italian side want £8 million for the 29-year old Uruguayan who played in all four of his country’s World Cup games.
Gonzalez would be the Dutchman’s eighth signing this summer and would take his spending to £55 million as he looks to fix his dilapidated squad.