Brendan Rodgers' side have persevered through a conflicting season however keep alive their expectations of lifting flatware come the finish of the mission.
The hosts came nearest to breaking the halt on the stroke of half-time however exuberant winger Harvey Barnes shook the crossbar following a one-two with Kelechi Iheanacho.
PSV ought to have started to lead the pack in only the second moment when Mario Gotze sidestepped the offside snare however Kasper Schmeichel spread himself wide to deny the German World Cup victor.
The different sides meet at the Philips Arena in the second leg next Thursday for the option to meet Roma or Bodo/Glimt in the last four.
That tie saw Norwegians Bodo/Glimt score in the 89th moment to take a 2-1 benefit into the subsequent leg.
Remember Thursday's European activity
Chances at a higher cost than normal
This was just Leicester's subsequent European quarter-last following their Heroes Association takes advantage of five years prior which finished when they were taken out by Atletico Madrid.
PSV are the more experienced side in mainland contest and won the old European Cup back in 1988.
Roger Schmidt's side are second in the Eredivisie, four focuses loose of pioneers Ajax, and are playing in their third European rivalry of the time.
They were taken out of the Bosses Association end of the season games and afterward came third in their Europa Association gathering to drop down into this recently framed rivalry.
Also, Leicester will have a lot of idealism going into the following week's tie realizing PSV have lost nine out of their beyond 10 quarter-finals in Europe.
After a watchable first a large portion of, the challenge disappointingly dwindled and eventually there were only three shots on track between the sides.
Gotze's initial exertion, upset by Schmeichel, was their main shot on track in the whole challenge, while goalkeeper Yvon Mvogo's recoveries from Timothy Castagne and James Maddison were both agreeable to manage.
Iheanacho, in the interim, botched a brilliant opportunity when he went through on objective however dinked his shot wide, while the Nigerian additionally shot askew in the subsequent period.
Britain Under-21 global Noni Madueke blasted over from a promising situation for the guests and Ricardo Pereira was fortunate not to surrender a punishment when he stumbled PSV captain Cody Gakpo in the case, yet the official waved play on.
The Dutch side paused for a minute and appeared to be content to take a draw, with Leicester attempting to set out goalscoring open doors, however the outcome broadened their unbeaten run at home in Europe to 10 games.
Last season's FA Cup champs are out of that opposition this term and are right now tenth in the Head Association, leaving the Europa Gathering Association as their main possibility lifting a prize this year.Leicester supervisor Brendan Rodgers: "We have adequately shown and seen to the point of realizing we can go there and win.
"Anyway it would have been, it was continuously going to be tight. You'd very much want to win it, yet it wasn't to be.
"We showed our versatility protectively and we'll go there with enough expectation that they'll presumably open up a smidgen more, which will give us a touch more space. It's finely adjusted, I thought it was a decent game.
"With somewhat more artfulness and accuracy in our passing then we could have had the option to open the scoring. We're as yet in a decent spot."
PSV manager Roger Schmidt: "I've seen it, it was an unmistakable punishment. I hate the VAR so I can't say anything negative. It was a punishment, yet it's essential for football where arbitrators go with wrong choices.
"We acknowledge it and we need to zero in on the following week. We played a great game. We needed to endure at times, yet we played against a great adversary.
"Altogether, I'm exceptionally content with the presentation. In the principal half we had great ball wins, yet in the advances we weren't adequately speedy to be accessible for forward passes."
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