The White Hart Lane boss has claimed that he had the chance to sign the prolific German striker but felt the existing striking options at the club did not make a move worthwhile.
Klose joined the Roman outfit last season and hit 16 goals in 35 appearances for the Biancocelesti, who Spurs face in the Europa League on Thursday.
Whilst Villas-Boas appreciates the Germany international's talents, he did not enter negotiations with the player as he is satisfied with his current striking options.
"We were offered [Miroslav] Klose by a FIFA agent, but there was never any real negotiations," the Portuguese told Italian newspaper Gazzetta dello Sport. "Klose is a good player, but I have three very good strikers in [Jermain] Defoe, [Emmanuel] Adebayor and [Clint] Dempsey."
Tottenham made an early exit from the Europa League last season, and Villas-Boas has insisted he wants to make a strong impression in the competition that he won two seasons ago with Porto.
However he is wary of the talent of the Italian side, which has made a perfect start to the Serie A season, joining Juventus and Napoli at the summit after winning its first three games.
"It will be a difficult match," he said. "The Italian championship is one of the toughest in the world, and whoever is at the top [of the division] needs to be addressed with the utmost concentration.
"Only those who watch football with superficiality could underestimate Lazio. There are important players. [Cristian] Ledesma, for example, is one of my favorite players. Then there is Hernanes. I expected to find him in a top-end club, but instead Lazio kept him."
Tottenham and Lazio are joined in Europa League Group J by Panathinaikos and Slovenian minnows NK Maribor.
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