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 Rome outfit last season and hit 16 goals in 35 appearances for the Biancocelesti, who Spurs face in the Europa League on Thursday.
And 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.
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"We were offered [Miroslav] Klose by some Fifa agent, but there has never been a real negotiation," the Portuguese told Italian newspaper Gazzetta dello Sport.
"Klose is a good player, but I have very good strikers with [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 talents of the Italian side, who have made a perfect start to the Serie A season, winning all of their first three games.
He added: "It will be a difficult match. The Italian championship is one of the toughest in the world and who is at the top 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 and instead Lazio keep him."
Tottenham and Lazio are joined in Europa League Group J by Greek side Panathinaikos and Slovenian minnows NK Maribor.