The versatile attacker was one of the Saints’ standout performers throughout the season just finished, before injury curtailed his campaign and ended his hopes of a possible World Cup call-up a matter of weeks ago.
His fitness issues have prevented him from making the trip to Brazil, yet it is expected that with the recovery time the summer allows he’ll be back in action for the 2014/15 campaign.
This has alerted Spurs, who are long-term admirers of the 24-year-old.
The London club are thought to see the 17-goal man as a top quality addition as they plot to break into the top four next season after missing out on Champions League football the last two times of asking.
Tottenham may also move for Southampton’s manager Mauricio Pochettino, which could further open the door for Rodriguez to relocate to White Hart Lane.
The South Coast side may well be reluctant to let ‘J-Rod’ move on, with Liverpool closing in on captain Adam Lallana and Manchester United keen on Luke Shaw – both of whom made England’s 23-man World Cup squad alongside experienced striker Rickie Lambert.