The Brazilian centre-back has been an ever-present figure in Inter's backline since joining the Italian club from Bayern Munich in 2009 in a deal worth €7 million (£5.6m).
He signed a new contract last summer which binds him to the Nerazzurri until 2014, but his representative has said that the 34-year-old will switch clubs before next season.
"He has put an end to three great years at Inter and he feels it is time for a change," Sandro Becker told Lancenet.
"We have been taking care of this since last week and we will speak with Inter again on Wednesday.
"We shared our thoughts and Inter accepted it. Now we have to look for a new club.
"Lucio has only made friends where he has been. He was the one who decided to leave, but Inter understood him. It was a friendly decision."
|"He has put an end to three great years at Inter and feels it is time for a change. We shared our thoughts and Inter accepted it"
- Sandro Becker on Lucio
Becker then explained that his client's priority is to remain in Europe, but did not rule out a return to Brazil.
"His preference is to play in a big European league, but you never know," he added.
"There is a lot of interest from Brazilian clubs and Lucio knows that the 2014 World Cup will be played there.
"We do not know his future."
Lucio has played 105 games for his country since making his debut in 2000.