The 34-year-old Germany international has stated that a move to White Hart Lane was discussed late in the transfer window but that he chose to stay in Serie A instead
The 34-year-old, who has scored 64 goals in 124 appearances for Germany, moved to Vladimir Petkovic's side from Bayern Munich at the start of last season and underlined his desire to show "respect" by staying.
"Tottenham came looking for me, but I signed for Lazio until 2014 and I intend to respect that contract," Klose told sportal.it.
Spurs boss Andre Villas-Boas has just two strikers in his first-team squad at the moment, Jermain Defoe and Emmanuel Adebayor, having loaned out Harry Kane to Norwich for the season.
Tottenham also failed to complete a late deadline day swoop for Porto playmaker Joao Moutinho, although it did manage to secure deals to sign Fulham duo Mousa Dembele and Clint Dempsey.