In a match of few chances, Southampton's Shane Long was denied by Foxes goalkeeper Ben Hamer, making his first Premier League start of the season.
Ryan Bertrand drove wide from distance while Dusan Tadic also came close.
The best chance fell to Leicester's Jamie Vardy, seeking his 18th league goal of the season.
The striker latched on to a long ball but his effort was well saved by Alex McCarthy.
Southampton remain 18th, four points behind Swansea City, who have played a match fewer.
Leicester stay eighth.
Leicester: 28 Apr v Crystal Palace (A)
Southampton: 28 Apr v AFC Bournemouth (H)