The striker moved to the Championship club from Fleetwood Town before last season, going on to score just four goals in 26 appearances.
"Yes I did [nearly give up] to be honest with you," Vardy told BBC Late Kick Off Midlands.
"But I had a few chats with the gaffer (Nigel Pearson) and they constantly told me I was good enough and they believed in me and stuck by me. I am glad to be showing the faith they showed in me on the pitch."
This season Vardy has found the net 15 times in 33 appearances, helping Leicester to the top of the Championship and on the brink of automatic promotion to the Premier League.