The Reds are known to be in the market for a new centre-half, despite having secured two clean sheets during their opening two fixtures of the Premier League season.
Veteran Ivorian Kolo Toure has already arrived at Anfield this summer, while Daniel Agger is set to reject potential interest from Barcelona to stay put.
But, Rodgers is still keen to make at least one addition, with Alderweireld in his thoughts.
The Belgian is believed to be available for a cut-price £6m with his contract due to expire at the end of the 2013/14 campaign.
Ajax are aware that selling now makes financial sense, and are willing to do business with Liverpool – the same club they sold Luis Suarez to in 2011.
The 24-year-old has already rejected a move to Norwich this year, but it is believed that interest from a side of the Reds’ stature would be enough to see him leave Amsterdam.
Tottenham were thought to be keen, however their move for Romanian star Vlad Chiriches would appear to rule them out.
Liverpool are also keen on Sporting Lisbon’s Tiago Ilori and Kyriakos Papadopoulos of Schalke.
Liverpool fans, is Toby Alderweireld the right man for your defence? Or should Brendan Rodgers stick with Kolo Toure?
Have your say below!