Trapattoni,74, has been linked with a move to the Stadio Olimpico, with Lazio having won just one of their last six Serie A games.
"Am I going to Lazio? No," Trapattoni was reported as saying by Corriere dello Sport. "Those are just rumours that are unfounded.
"With regards to my future, there have been some conversations (with interested parties) and I will try to make the right choice.
"Italy is a marvelous country in which I've had success and satisfaction."
Trapattoni has been out of a job since stepping down as Ireland manager in September after five-and-a-half years at the helm.
The former Italy coach is one of only five coaches to have won the league title in at least four different countries (Italy, Germany, Portugal, and Austria).
Trapattoni has guided AC Milan, Juventus, Inter Milan, Cagliari and Fiorentina in Serie A during his 39-year coaching career.