The Saints striker enjoyed a successful campaign, scoring 15 league goals in 33 appearances - however his chances of making it to the World Cup with England were dashed when he ruptured his ACL last month.
Having undergone surgery Rodriguez is unlikely to play again until the end of the year, but according to the Daily Mail that won't put Tottenham off making a bid for the 24-year-old.
The paper claim that Spurs are looking at signing English players this summer to balance out the amount of foreigners they have on their books. Tottenham spent more than £100 million on seven players last summer and aren't expected to splash the cash as heavily this time round.
Rodriguez's potential switch to White Hart Lane could be helped if Southampton manager Maurico Pochettino also swaps the south coast for north London.
The Argentinian has been linked with the hot seat at Tottenham, with current incumbent Tim Sherwood set to be shown the door.
Southampton enjoyed a fine Premier League season and finished 8th - although they are now under siege with a host of clubs said to be intent on snapping up their best players.
Manchester United are said to have made an offer worth around £27 million for Luke Shaw, while Liverpool are reportedly keen on club captain Adam Lallana.