The England international has been one of the stars of the 2013/14 campaign with the Saints, and was being tipped to make the Three Lions’ World Cup squad before a knee injury ended his campaign prematurely a few weeks ago.
Even with his fitness concerns, a number of top clubs are rumoured to be looking at summer moves for the 24-year-old, including Liverpool and Manchester City.
But it is understood that Spurs are paying the closest attention to the versatile attacker as they step up their transfer plans.
Even with the future of Tim Sherwood up in the air, chairman Daniel Levy is believed to be ready to sanction serious moves in a bid to avoid the problems that plagued the London club last year.
Although Southampton have indicated that top stars will not be sold, it is rumoured that significant bids could lure Rodriguez away from the South Coast.
As well as J-Rod, Adam Lallana and Luke Shaw are thought to be targets for clubs in the Premier League’s top seven places.