Ranieri replaced Eusebio di Francesco after his dismissal earlier this year, returning to Roma for a second time on a deal to the end of the season.
“The embrace of the fans will always stay with me, as will the pride of having led the team of my heart. That'll never change," he told Sky Sport Italia.
“I think a lot of Roma's progression depends on the stadium and whether it's built. It's only logical that a club want to do things properly.
“They could raise more revenue by having their own stadium. They're working well, but the fans want results on the field.
“The important thing now is to find a Coach and sporting director and let everyone row on the same side.
“Roma can fight for fourth place. Football is great because nothing is written. I think I proved that at Leicester and I wish them all the best."
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