The 25-year-old stopper, who is currently on loan at Palmeiras, joined Barca in 2008 in an €8 million deal, but he has not yet featured for the Catalan club.
After spending the last three years on loan at three different clubs, Henrique's chances of ever making Barca's first team look slim, and Gremio are reportedly interested in signing him on a permanent basis.
It is believed that the Porto Alegre-based club are willing to offer €2m for the defender, a fee which will be paid in four different instalments during the course of 2012.
Henrique played an important part in the Palmeiras side who finished 11th in the Brasileirao, 21 points off the top of the table.
Starting last month and continuing all through January, Goal.com will publish extracts from Graham Hunter's highly-anticipated book, 'Barca: The Making of the Greatest Team in the World'. In the latest extract, he looks at Pep Guardiola's early beginnings at Barca B in the Spanish third division ahead of his meteoric rise to world domination with the first team. Don't miss it!