The 29-year-old Rennes ace arrived in England on Monday and is training with The Foxes for the rest of this week.
"Jocelyn has been highly recommended to us and we will have a good look at him this week," said assistant manager Micky Adams.
"From what I've seen already he certainly looks a talented boy. Hopefully he can do enough to impress us and we can take it from there."
However, even if Gourvennec does impresses he may not end up at Filbert Street as Metz are also keen on the for the former Marseille ace.
Rennes general manager Gerard Lefilatre confirmed the interest of the other French club, saying: "The Metz option is possible."
Gourvennec is missing training with Rennes this week in order to undergo his trial with Leicester.
Meanwhile, the club are to appeal to the Home Office for a work permit for Chinese striker Zhang Yuning.
As expected the club have had their initial application turned down for the second time, after their claim was re-assessed last week.
