Rodgers, 49, has come under pressure having failed to win any of the first seven games of the season, leaving Leicester bottom of the Premier League.
However, the former Liverpool boss is confident he can turn things around.
"I'm the best person to help this team move forward," said the Northern Irishman.
"I haven't [spoken to the owners]. The ownership trust me and expect I will turn it around. If they don't they will tell me.
"If you are bottom and have lost six out of seven you are not going to be flavour of the month. You don't isolate yourself, that's important, I love working with these players.
"I believe, like last season, we will come good. It has been a tough start but I see these players work and it ultimately gives me strength."