Puygrenier, who played seven Premier League games whilst on loan at Bolton Wanderers in the 2008/09 season, is currently with Russian club Zenit St Petersburg but has been training with Monaco where he has twice enjoyed loan spells.
The central defender, now 29, started his career with Rennes before moving to Nancy and then, in 2008, Zenit St Petersburg. During his time there he's had very limited opportunities to establish himself, went to Bolton and then has played more games during his two loan spells with Monaco.
He made his Bolton debut in January 2009 in a 1-0 home defeat against Manchester United. He scored once during in his seven games with them, the first goal in a 3-2 win against Spurs at the end of January.
There has been no confirmation from Burnley but French news sources suggest he'll be heading for Burnley tomorrow for the trial.