The club's 1-0 win over FC Copenhagen on Tuesday was their third in a row in the Champions League -- the best start by a British club in their debut season in the competition and a level of consistency matched by only a handful of clubs since it began.
They have yet to concede a goal and progress to the knockout phase is almost guaranteed at the halfway stage.
Nagging away in the background though is Leicester's worrying start to the defence of their Premier League title which has left Claudio Ranieri's side only two points above the bottom three.
They have eight points from eight games -- seven less than they had at this stage last season and one less than they have already managed in three Champions League games.
Teething problems perhaps as they juggle the demands of European football with the 'bread and butter' of the Premier League. But Ranieri will be well aware that a poor start can quickly lead to a relegation battle in England's top flight.
"From one side I'm very proud," Ranieri said of his side's lop-sided start to the season.
"From the other side, when I think of the Premier League, I'm very, very angry. But it's OK because in my career this has happened. When for the first time you play in a big competition, you lose something when you go back in your league.
"This is normal but we want to change this way. It's just psychological. When we play in the Champions League our special qualities switch on."
"The Premier League is our priority," added Ranieri. "We have to stay calm and change our mentality and focus for the Premier League."
Leicester's struggles in the Premier League continued in a 3-0 defeat by Chelsea at the weekend, meaning they have conceded 13 goals in their four away matches so far.
Last year they leaked only 18 on the road all season.
The sale of holding midfielder N'Golo Kante to Chelsea has been a factor in Leicester's fragility.
In attack too they have problems with Jamie Vardy managing only two Premier League goals so far compared to nine this time last year. Algerian playmaker Riyad Mahrez, scorer of the winner against Copenhagen, is also struggling domestically, netting just once from the penalty spot so far this season.
He was 'rested' against Chelsea, a move vindicated by his impressive display on Tuesday.
But with Champions League progress all but assured, Ranieri's focus must now switch to the domestic front where it was always going to be a difficult task to back up last year's astonishing exploits.
"You spend a lot of mental energy in the Champions League. When you come back you are a little down but this is normal," he said. "We want to change this mood because it is important now for us the Premier League."
Leicester host Crystal Palace on Saturday.
(Editing by Mitch Phillips)
