Agger, who joined the Reds from Danish side Brondby in 2006, only signed a new two-year extension to his current contract in October of last year.
Even though the 28-year-old is contracted until 2016, reports in Spain and Denmark suggest that Martino is weighing up an offer for the defender.
The Danish international came close to joining Barcelona last summer, until a change of heart from former manager Tito Vilanova scuppered the transfer.
Martino's attentions turned to the Liverpool ace after a move for Chelsea defender David Luiz was rejected by Blues boss Jose Mourinho.
The former Real Madrid coach dismissed their interest insisting that there would be 'no chance' of Luiz leaving Stamford Bridge regardless of the size of the bid from the La Liga champions.