Talks between Lucio and Inter are set to continue after so far failing to agree terms over a new contract.
The Brazilian is only tied to the Nerazzurri until 2012 and both parties want to continue their relationship.
However, according to reports, there is a difference of opinion regarding both the length of the contract and the salary.
Lucio is asking for a deal until 2014, but the San Siro giants are proposing an agreement until 2013 instead.
The Brazilian, who turned 33 earlier this month, joined the Nerazzurri in the summer of 2009 from Bayern Munich.
It is understood that the South American currently earns €3m a campaign in Italy.
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