Media playback is not supported on this device
Leicester's maiden top-flight title was a huge surprise last season but the Italian, 64, insisted his team has a "strong foundation".
"Last season we made something which is hard to repeat but I want the maximum," Ranieri said.
Leicester face Manchester United in the Community Shield at Wembley on Sunday.
"I am very curious what we can do now," he added.
"I spoke with my players and I said: 'I know you very well now and I want more. I want more than the maximum from last season.'"
Ranieri has added five players to his squad this summer, including club-record £16m signing Ahmed Musa, and £13m midfielder Nampalys Mendy.
Last season's top scorer Jamie Vardy has committed his future to the club, rejecting a transfer to Arsenal.
However, N'Golo Kante has left for Chelsea in a £30m deal, while reports suggest Arsenal are also interested in Premier League player of the year Riyad Mahrez.
Leicester City boss Claudio Ranieri has told his team "forget what we achieved - I want more" before their Premier League title defence begins.