The Saints are determined to keep the 24-year-old at St Mary's.
The north London side had been linked with the Frenchman all summer but Schneiderlin remained a Saints player and has made a strong start to the new Premier League season.
Mauricio Pochettino, though, is said to still hold strong interest in bringing the midfield man to White Hart Lane during the January transfer window.
As such, the Daily Mirror are reporting that Southampton are readying a new contract offer for Schneiderlin - which comes with a big salary increase.
|Team||Pos||Chances Created||Goals||Accurate Passes||Tackles Won||Apps||Mins|
As Opta stats show, before today's clash with Spurs, Schneiderlin has easily been the Saints' most influential player in the league (barring top scorer Graziano Pelle, of course).
The Frenchman has created five chances but, more impressively, scored three goals.
His biggest contribution has predictably come from midfield, however, with Schneiderlin having completed 376 passes so far and won 19 tackles.
It is no wonder Southampton want to keep the 24-year-old at St Mary's, then, just as it is no surprise that Pochettino still holds plenty of interest in the midfield maestro.
Expect the Schneiderlin saga to rage on, although the Frenchman putting pen to paper would certainly put Ronald Koeman's side in a much stronger position.