Gonzalo Higuain missed the best chance to break the deadlock at the King Power Stadium on Sunday, but Chelsea ended the campaign above Tottenham after the Champions League finalists drew 2-2 home to Everton.
Kasper Schmeichel made a great reaction block to deny Ross Barkley in the third minute before the Leicester goalkeeper dived low to his left to keep out Willian's tame effort.
James Maddison and Higuain fired off target in a first half played at low tempo but Leicester should have struck first, Jamie Vardy playing a poor pass at the end of a quick break.
Chelsea wasted an even better chance to open the scoring on the stroke of half-time, Higuain making a mess of a seemingly straightforward opportunity created by Marcos Alonso.
Barkley pulled a shot wide after the restart before a crucial Cesar Azpilicueta intervention prevented Vardy from having a clear sight of goal.
Sarri brought on Eden Hazard with 21 minutes to go while Leicester introduced title-winning duo Shinji Okazaki and Danny Simpson for farewell appearances.
But, with little riding on the result, the match petered out, although Youri Tielemans shot over late on, Chelsea's attention having seemingly turned to their Europa League final against Arsenal in Baku.
What does it mean? Blues finish third
Chelsea rested key players including Hazard and Kepa Arrizabalaga with an eye on the May 29 showdown with the Gunners, and Tottenham's failure to win ensured Sarri's decision did not backfire.
Leicester end a campaign that will be remembered for the passing of chairman Vichai Srivaddhanaprabha in ninth, having made good progress under Brendan Rodgers.
Ndidi solid in Foxes midfield
Chelsea kept Leicester under pressure in the first half but the Foxes were able to push up the pitch after the break, mostly due to the steady influence of Wilfred Ndidi in midfield.
Higuain in last chance saloon
Chelsea's hunt for a successor to Diego Costa looks set to continue, with Higuain failing to make his mark. The striker got his feet in a muddle as he wasted a simple opening late in the first half.
Key Opta Facts
- There has been just one goal scored in the last three Premier League meetings between Leicester City and Chelsea.
- This was Chelsea's fourth goalless draw in the Premier League this season, their most since 2013-14 (also four).
- Chelsea won just two of their last nine Premier League away games this season (W2 D2 L5), drawing their last two.
- Leicester manager Brendan Rodgers has faced Chelsea more often than any other Premier League side without winning (nine games – W0 D5 L4).
- Chelsea ended the season in third position, the 13th time in the last 16 seasons they have finished in the top three of the Premier League.
Chelsea have a trip to Boston for a post-season friendly before taking on Arsenal in Azerbaijan. Leicester will hope to push for a top-six finish under Rodgers next term.