The Germany international, who is out of contract at the end of the season, has been upset by the claim that he has opened talks with the Bundesliga outfit
It was claimed earlier this week that the Germany international, who will be a free agent next summer, was considering a return to the Bundesliga with Sami Hyypia's side.
However, Klose, who has also been linked with a MLS move, has angrily rejected the implication that he has been speaking to other clubs.
"What they have written are lies," the 35-year-old forward told Lazio Style Radio. "The first club I'll speak with will be Lazio.
"I spoke four months ago and I spoke of the chance to go to America, but it's normal because my contract expires at the end of the season.
"But the first team I'll speak with is Lazio and when the right moment comes, we'll sit down and talk.
"But regarding Leverkusen, it's all lies. I never talked with this newspaper, which I do not know.
"This worries me because the fans can get the wrong idea. Now it is important for me to play and give everything for the team.
"I'm here to tell you the truth; the rest is all lies."
Klose has been out of action with a shoulder injury sustained against Parma earlier this season but the former Bayern Munich attacker says he is now ready to return to action.
"I'm fine," he explained. "I'm not 100 per cent, but the shoulder does not hurt me more. It's better.
"I do not feel pain and I now need games. I want to play. We have two games before the end of the year. I want to play in those - and to win them."
Lazio have struggled without Klose and currently sit 12th in Serie A ahead of Sunday's meeting with Livorno at the Stadio Olimpico.