The 36-year-old forward struck his 16th goal in his World Cup career in the 7-1 demolition of hosts Brazil on Tuesday, a strike that has made him the competition's all-time leading scorer.
"Now we have a champion who has scored the most goals in World Cups," Lazio president Claudio Lotito said to Italian radio station Rai Due.
"The figure he had to reach, he has already done so, regardless of whether or not he scores in the final.
"In order to receive offers for a player, he must be placed on the market and Klose is not for sale."
Lazio celebrated Klose's achievement with a tweet that said: "Sixteen goals in World Cups, the best of all time. Miro Klose enter history. Miro Klose is the history."
Klose, who moved to Lazio from Bayern Munich in 2011 and has scored 35 league goals since then, is under contract with the Rome-based outfit for a further season.