Lucio is said to be in advanced negotiations for a contract extension that will see him end his career at Inter.
The Gazzetta dello Sport suggests that director Marco Branca has been in talks for some time over a new deal.
It would tie the Brazilian to the club until 2013 with an option for the 2013-14 campaign too.
That would be a significant bond, considering Lucio is already 32 years old.
Earlier this month, the player had been linked with a return to his former club, Bayern Munich.
Think you know your Italian football? Share your knowledge, tips and comments to win cash prizes in OLBG's tipster competition - £11,000 to be won monthly!