The 35-year-old has been in Edinburgh for talks with the Capital club following the expiry of his contract with Bordeaux who he won the Coupe de France with in 2013.
It follows the news that Hearts have taken former Burton Albion goalkeeper Jon McLaughlin on trial for a week.
The French stopper has played more than 350 times in Ligue 1 for French giants Marseille as well as Les Girondins and Toulose. He also spent time on loan at Crystal Palace.
Bordeaux spent more than £7 million on Carrasso in 2009 and was handed his first and only french cap three years later in a friendly against Poland. He was a regular around the French national team, mainly as the third-choice goalkeeper.
He was first-choice keeper for Bordeaux last season and would be seen as the experienced keeper the club require.