The online bookmaker have suspended betting on Rodriguez's next club after taking bets on Tottenham signing the forward at as short as 1/6.
Dejan Lovren and Calum Chambers became the latest Saints players to make their move, to Liverpool and Arsenal respectively, meaning the south-coast club have allowed five of their most prized asset to depart, with Luke Shaw, Adam Lallana and Rickie Lambert also leaving.
Sky Bet initially had the Saints as 14/1 outsiders for relegation when they opened betting at the start of the summer but now make them 11/2 for the drop.
The St Mary's outfit finished eighth in the Premier League last season but are now the same odds to go down as West Ham, who finished 16 points behind them.
Sky Bet's transfer odds are cause for further concern with Morgan Schneiderlin and Jay Rodriguez odds-on to join Tottenham this summer, while record signing Dani Osvaldo is also expected to depart.
Sky Bet Football Trader Jamie Munro said: "The combination of their mass sales and the fact that we’ve seen more money on them than any other club in our relegation betting has forced us to slash their odds considerably.
"It's unprecedented to cut a Premier League club's relegation odds by more than half without a ball being kicked but the betting in our Transfer Specials suggests the situation is only going to get worse.
"Schneiderlin and Rodriguez have been well backed to join Mauricio Pochettino at Tottenham and there's little to suggest reinforcements are on the way, while Ronald Koeman's lack of Premier League experience is also cause for concern."