The Foxes were confirmed as Premier League champions on Monday evening as Tottenham Hotspur failed to beat Chelsea at Stamford Bridge.
It is now being described as the greatest achievement in football, if not all sport, given that practically the same squad only just managed to avoid relegation last season.
After their unlikely triumph, many are of course asking if Leicester can do it again but Parlour says he believes they will be happy to just avoid relegation.
“Expectation? I don’t think it will go up that much next season,” he told Sky Sports.
“You’d expect it to go through the roof but I think the Leicester fans will look at it and if they come fourth from bottom next season I think they would still be delighted.“
How Leicester’s future turns out will almost certainly rest on whether they can keep hold of their key stars and even their manager this summer.
The likes of Jamie Vardy, Riyad Mahrez and N’Golo Kante have been among their standout performers and that has not gone unnoticed across Europe.
The latter two have already been linked with potential moves to some of the elite sides in Europe and it will be interesting to see whether they stay to continue what they have started at the King Power Stadium.