BBC Radio Humberside claim that the 34-year-old World Cup winner was flying into England on Thursday to discuss terms with the Tigers.
He had two spells in the Premiership with Middlesbrough, and also played for Atletico Madrid and Celtic.
He was released by Brazilian club Flamengo last month following his angry reaction to being substituted during a Copa Libertadoes match.
"We've got a lot of business in the top drawer, which is about 90 to 95 per cent done, but I won't be announcing anything until the deals are 100 per cent completed," Tigers boss Phil Brown told PA Sport.