Ranieri opted instead to take charge of the Greek national side in July 2014 - just weeks after Dutchman Ronald Koeman accepted the Saints job.
However, the Italian lasted just four months in the role and was sacked after Greece suffered a shock defeat to the Faroe Islands in the Euro 2016 qualifying group.
SUBMIT AN ARTICLE
Apply to become a GMS writer by signing up and submitting a 250 word test article: http://gms.to/haveyoursay5
When asked if he had held talks with Southampton, Ranieri said: "Yes. I was interested, but after that there was also the Greece job - and I made a mistake.
"It was important that it was the right moment - and it (Southampton) wasn't the right moment for me."
Ranieri takes his Leicester side to St Mary's tomorrow to take on a Southampton side who have won their last two games 3-1, against Swansea and Chelsea.
A win for the hosts tomorrow would see them leapfrog the Foxes. However, they will have to do so without the services of Republic of Ireland international striker Shane Long.
The 28-year-old suffered an ankle ligament injury in the Republic's recent defeat against Poland and is expected to be out for two to four weeks.
Ranieri and his Leicester side will fancy their chances, though, looking to build on their impressive start and fifth place in the Premier League.