Reports suggest Saints are asking £27million for midfielder Schneiderlin, who joined the club from Strasbourg in 2008 and played a key role in their rise from League One to the top-flight.
The 24-year-old represented France at this summer's World Cup and has attracted interest from Arsenal, although he is understood to favour a move to Spurs so he can work with Pochettino again.
The former Argentina international is also in for Rodriguez, despite the England forward currently being sidelined by an anterior cruciate ligament injury.
The 24-year-old has been at St Mary's since joining from hometown club Burnley two years ago and made his Three Lions debut in November's friendly against Chile.
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