The Frenchman joined the Foxes from Stade Reims in August on a short-term contract until January.
But the 27-year-old, who made his full debut for Nigel Pearson's in-form side against Middlesbrough on Tuesday, is determined to stay in England for the foreseeable future.
Kermorgant told the Leicester Mercury: "I hope to stay. It was difficult for me to sign for a long time because I was injured, but now I am fit.
"In a few weeks I will talk to the manager and, if he wants to keep me, perhaps I will stay here for a longer time. I like English football and it was the reason I came here.
"It is a new life here and a big challenge for me, and I like that. I think English football suits my style."