Arsenal completed the signing of highly-rated right-back Calum Chambers on Monday afternoon, less than 24 hours after Dejan Lovren joined Liverpool in a £20million deal.
The Croatia international followed Rickie Lambert and Adam Lallana in moving to Anfield, while teenage left-back Luke Shaw recently departed for Manchester United.
Those transfers came in the wake of manager Pochettino and his staff leaving for Spurs, where two of his former Saints charges could be plying their trade next term.
Press Association Sport understands Tottenham have stepped up their interest in Schneiderlin and Rodriguez, with the pair edging closer to deals taking them to White Hart Lane.
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.
Their exits would be another hammer blow to recently-appointed manager Ronald Koeman, who is also expected to sell disruptive club-record signing Dani Osvaldo in the coming weeks.
Work is afoot to bring in replacements but so far only two have arrived, with Dusan Tadic joining from FC Twente before Graziano Pelle arrived from Koeman’s former club Feyenoord.
Southampton executive director Les Reed has come under fire for this summer’s transfer activity and attempted to allay fans’ fears after Chambers’ departure to Arsenal.
“Our position remains unchanged in that we are determined to keep our best young players at the club, as is evidenced by the decision to award Harrison Reed a new long-term contract last week, adding to the list of committed young professionals like James Ward Prowse, Sam Gallagher, Jack Stephens, Jordan Turnbull, Matt Targett, Sam McQueen and others who have seen plenty of first-team activity recently,” he said on the club’s official website, www.saintsfc.co.uk.
“We have an abundance of talent in the academy coming through, and everybody at the club is continuing to work hard on bringing in quality new players as we build a team capable of taking us further forward in the coming seasons.
“It is important in the transfer window to remain calm, resilient and above all patient. We have targets, and we are working hard to get them across the line.”