According to the Daily Mail, the Reds will look to bring in the Belgium international should they qualify for the Champions League and Spurs fail to.
Despite being in free-scoring form throughout the season, the Anfield side have at times looked vulnerable in defence.
And Rodgers believes Vertonghen - who arrived at Spurs in 2012 from Ajax - is the man to sure up his leaky back-line.
Able to play in the centre or on the left of defence, the former Ajax captain would bring versatility to Rodgers' squad, and at 26 would offer years of service.
The experienced left-back is out of contract in the summer, and having fallen behind Cesar Azpilicueta in the pecking order, there is no guarantee that the Blues will offer him a new deal.
Rodgers currently has both Jose Enrique and Aly Cissokho, although neither have entirely convinced the former Swansea boss.
After running out convincing 3-0 winners over Southampton, many are now tipping Liverpool as genuine contenders for the league title.
Without the added distraction of Europe or cup competitions, Rodgers' men can focus entirely on their league form.
Just one point off leaders Chelsea, Liverpool remain unbeaten in 2014 in the league.
Next up will be a difficult trip to Old Trafford to face a struggling Manchester United side.