Saints’ legend Matt Le Tissier believes the England international will look to see how the likes of Luke Shaw at Manchester United, and Rickie Lambert at Liverpool, fare this season before making a decision over his future.
Southampton also lost Dejan Lovren and Adam Lallana to Liverpool, while Morgan Schneiderlin attempted to force a move to Tottenham towards the end of the transfer window but was unsuccessful in his efforts.
Despite losing several key players, and their influential manager Mauricio Pochettino, the south-coast club have exceeded expectations this season and currently find themselves second in the Premier League table having taken 13 points from a possible 18.
Le Tisser optimistic
And when asked whether Rodriguez, who was strongly linked with a move to Arsenal and Tottenham during the summer months, will opt to stay put at Southampton under new manager Ronald Koeman, Le Tisser responded optimistically.
"I'd hope so,” he told Starsport. "We aren't looking in too bad a shape this season - and Jay's still got to come back.
"If the seasons don't go well for the lads that have left, he could look at that and think sometimes the grass is not greener on other side and we can keep hold of him here.
"The club is in sound financial state right now.
"They did good business over summer and don't need to sell."
Ex-Southampton stars struggling
Lambert has endured a frustrating start to his Liverpool career, having failed to have made a single Premier League start to his new club, while Lovren has looked unconvincing in central defence.
Lallana is also taking time to settle into his new surroundings at Anfield following a lengthy spell on the sidelines, while Shaw has admitted that he’s already feeling the pressure of being a Manchester United player.
Rodriguez faces more competition
Rodriguez, 25, scored 17 goals in 39 appearances last season and almost certainly would have been part of the England squad for the World Cup finals in Brazil had he not ruptured an anterior cruciate ligament two months prior to the showpiece international tournament.
But despite his excellent season with Southampton, he arguably faces even more competition for a starting spot when he returns from injury.
Summer signing Graziano Pelle has already scored four goals in his first six Premier League appearances for the Saints and is quickly establishing his status as a fans’ favourite.
Pochettino will still be keen to bring Rodriguez to White Hart Lane when the transfer window re-opens in January, while Arsenal boss Arsene Wenger could also be tempted if Danny Welbeck fails to score goals on a consistent basis between now and the New Year.