Tottenham are in danger of being drawn into the turmoil at Southampton more than any other club that has headed to St Mary's to do transfer business.
Rodriguez is still a few months off of match fitness, while Schneiderlin, if he was to join, would be coming into a midfield overloaded with central midfielders.
This isn't to say either player would be a failure were they to move to White Hart Lane. Schneiderlin in particular has long been one of the Saints' top players, and featured for France at the World Cup this summer.
But Tottenham themselves have international players of some quality already in his role, who arguably just need a good manager and the right tactics to see an upturn in form so they can justify their place in Pochettino's side.
Sandro, Etienne Capoue, Paulinho, Mousa Dembele, Lewis Holtby - all are central midfielders capable of playing a little deeper and at the time of signing at the club, much celebrated. There are also younger stars such as Nabil Bentaleb and Tom Carroll that will have to be accommodated on some level.
Central midfield is not a spot that needs reinforcement, and a huge mistake for Daniel Levy would be becoming preoccupied in Tottenham's pursuit of the Southampton pair rather than signing for positions that are glaringly needed - a top quality out-and-out striker and a central defender.
Saints chairman Ralph Krueger has put his credibility on the line by strongly stating that both Schneiderlin and another Spurs target, Jay Rodriguez will not be leaving this summer.
“They are part of the core that we have decided to keep at Southampton," Krueger told Sky Sports News.
“Jay Rodriguez and Morgan Schneiderlin are not for sale and they will be a part of our club as we enter the new season.”
It led Schneiderlin to seemingly retort on Twitter: "6 years of an amazing journey #saintsfc DESTROYED in 1 hour !!!"
Krueger has already had his reputation tarnished somewhat by claiming in May that there would be no "mass exodus" from Southampton after Mauricio Pochettino left to take over at Tottenham.
Given that Rickie Lambert, Adam Lallana, Luke Shaw, Callum Chambers and Dejan Lovren have all successfully angled for moves out of the club since that comment, one could perhaps take his comments with a pinch of salt. However, while there remain doubts about several other Saints first teamers, Krueger would be loath to be made to look like such a fool once again.
Pochettino, and or Spurs may or may not have got the signal from Schneiderlin (and Rodriguez) that they are very much eager on linking up with their former manager, but the North Londoners would do well not to get too caught up in something that is surely set to get messy.
Some at Southampton may remember Tottenham pinching Glenn Hoddle in 2001 after the ex England boss enjoyed a short but promising spell on the South Coast. Hoddle promptly returned to his old club to sign up Dean Richards, then the Saints' star defender.
If Southampton are likely to dig their heels in with any club, and regarding any transfers, it will be with any moves to Spurs. Which may be a cause for concern for Pochettino and co considering that Arsenal are also said to be keeping an eye on Schneiderlin.
It would be a huge surprise if the Saints accept Schneiderlin's transfer request, and it is a big if as there are conflicting reports on whether the Frenchman has even made one, but Tottenham should just be prepared to wait out and see if there is any resolution to the situation, rather than be drawn to making gigantic bids that may just convince Southampton to warm to the idea of selling the 24-year-old.