Klose started in Germany's 1-0 win over Argentina on Sunday, and came off with just minutes to go of the 90 to an extraordinary standing ovation.
"My most sincere congratulations to Germany and to Miroslav Klose," said Lotito.
"Yesterday, when Low called him off, the standing ovation that greeted his exit was amazing.
"It was a moment that touched the heart of every Lazio fan. Klose is without doubt the last of a generation of players that we are likely never to see again.
"He combines determination, commitment and hard work to achieve his goals.
"Klose is the past, present and future rolled into one.
"From my part, I do not hide my hope that he will finish his career with Lazio. That would be a great source of pride for me."
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