After falling out of favour at Anfield the veteran goalkeeper has returned to South America as he aims to push for a place in the national side's 2014 World Cup squad
The 33-year-old moved to Anfield in 2011 when the Reds paid Roma €1.5 million for his services, but only made four appearances since his arrival.
His last appearance for Liverpool was in the 1-0 defeat at Swansea on the final day of the 2011-12 season.
And the keeper has since fallen down the pecking order behind Pepe Reina and Brad Jones, with Jones deputising recently during an injury spell for Reina.
Doni has won 10 caps for Brazil and was in the squad for the 2010 World Cup in South Africa.